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Geometric models have emerged as an important tool in the representation theory of algebras. Surface models associated to gentle algebras have been particularly fruitful in advancing our understanding of their module and derived categories. We give an overview of some of the theoretical advances that geometric surface models for the derived categories of graded gentle algebras and their connections to Fukaya categories of surfaces have made possible.
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"description": "Mural Arts Philadelphia has partnered with the Outreach Committee of the International Conress of Mathematicians (ICM) to create an indoor mural which is displayed at the 2026 ICM convening at the Pennsylvania Convention Center. This mural has engaged local students of the Mural Arts Foundations & Innovation program as well as local artist Oluwafemi as he directed them during the 2025 - 2026 school year to fabricate this piece.
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This talk and view of the documentary will take place on the Benjamin Frankling Stage located within Hall E.
This talk will offer a behind-the-scenes look at the making of Contours of American Mathematics, a special exhibit exploring the history of 18th, 19th, and 20th century math as interpreted through the collections of the American Philosophical Society (APS) in Philadelphia. Curated by Karen Parshall (Commonwealth Professor of History and Mathematics, Emerita, at the University of Virginia) and created in collaboration with APS staff, the exhibit explores the mathematical contributions of figures including Benjamin Franklin, David Rittenhouse, Nathaniel Bowditch, James Joseph Sylvester, Emmy Noether, Mina Rees, and John von Neumann among many others. The presentation will highlight the curatorial process involved with creating both an in-person and digital exhibit and will include reflections on some of the challenges and opportunities involved with displaying a lesser-known aspect of the Society’s archives. By sharing this work with the ICM community, the presenters hope to increase the use of these collections by historians and mathematicians alike and offer a potential model for future collaborative projects.
Film Directed by George Csicsery
Journeys of Black Mathematicians: Creating Pathways is the second installment of a two-part documentary series which reflects the mathematical excellence of contemporary Black mathematicians. Featuring over 50 individuals representing a panoramic view of greatness in mathematics and STEM, these films seek to inspire today’s Black and minority graduate and college students as well as K-12 children across the USA and around the world who are developing the confidence that they too can become stellar mathematicians and STEM researchers.
Panelists
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- Nathaniel Whitaker, University of Massachusetts
- Sylvester James Gates, Jr., University of Maryland
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\"A Method for Constructing D-Distance (anti)magic Graphs\" by Anak Agung Gede Ngurah (13 - Combinatorics)
\"Constructible twin-sets in distance-hereditary graphs\" by Martín Safe (13 - Combinatorics)
\"On Regular Ramsey \\((mK_2, H)\\)-Minimal Graphs and Their Extensions\" by Kristiana Wijaya (13 - Combinatorics)
\"Some Aspects of Probability Related to the Riemann Hypothesis\" by Andrey Feuerverger (3 - Number Theory)
\"Modular Symmetries and Identities for Rank-Type Partition Statistics\" by Rishabh Sarma (3 - Number Theory)
\"Infinite tensors meet model theory\" by Alessandro Danelon (4 - Algebraic and Complex Geometry)
\"Conductor-Discriminant Inequality for Tamely Ramified Cyclic Covers of the Projective Line\" by Connor Stewart (4 - Algebraic and Complex Geometry)
\"A Simplified Rotation Algorithm of a Vector in Three Dimensions\" by Sanji Sun (4 - Algebraic and Complex Geometry)
\"The spin Dolbeault-Dirac operator on the quantum Grassmannian $Gr(2,4)$.\" by Fredy Diaz Garcia (7 - Lie Theory and Generalizations)
\"The classification of right alternative and noncommutative Jordan superalgebras\" by Abror Khudoyberdiev (7 - Lie Theory and Generalizations)
\"Besov Spaces and Statistical Properties of the Shift\" by Pedro Augusto da Silva Morelli (9 - Dynamics)
\"Hyperbolicity and Hausdorff Measures for Renormalization of Dissipative Gap Mappings\" by Márcio Gouveia (9 - Dynamics)
\"Large Deviations and Applications in Homogeneous Dynamics\" by Taehyeong Kim (9 - Dynamics)
\"Spectral Decomposition and Skew-Product for Group Actions\" by Keonhee Lee (9 - Dynamics)
\"Smoothness, Tangency and Uniqueness of Horospherical Foliations of Geodesic Flows\" by Edhin Mamani (9 - Dynamics)
\"A Discrete-Time Nonlinear Phytoplankton-Zooplankton Model with Toxin Release\" by Sobirjon Shoyimardonov (9 - Dynamics)
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Film: 3Blue1Brown (3b1b) is primarily a YouTube channel focused on explaining math visually.
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Let \\( C(X) \\) denote the lattice-ordered algebra of real-valued continuous functions on a realcompact space \\( X \\). Given a function \\( \\psi \\in C(\\mathbb{R}) \\), we say that a bounded, identity-preserving linear functional \\( h \\) on \\( C(X) \\) is a \\(\\psi\\)-homomorphism if it satisfies\\[h \\circ \\psi = \\psi \\circ h.\\]A function \\( \\psi \\) is said to be realcompact if every \\(\\psi\\)-homomorphism from \\( C(X) \\) to \\( \\mathbb{R} \\) is simply an evaluation at a point of \\( X \\).Classical results by Hewitt and Shirota established that the square and the absolute value functions are realcompact. In this talk, we extend these results by offering a broader characterization of such functions. Quite surprisingly, it turns out that a function \\( \\psi \\in C(\\mathbb{R}) \\) is realcompact if and only if it is non-affine.This characterization also leads to a Banach--Stone type result linking the structure of function algebras to the topology of the underlying realcompact spaces.
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Colors of Math is an intellectually stimulating and beautifully shot film that invites us to look at mathematics from a new angle as the arena of the senses. To most people mathematics appears abstract, mysterious. Complicated. Inaccessible. But math is nothing but a language to express the world. Mathematics can be sensual. In this documentary, the beauty of mathematics, its sounds, colors, taste, and texture are revealed through the eyes of contemporary mathematical geniuses C´edric Villani, Aaditya V. Rangan, JeanMichel Bismut, G¨unter Ziegler, Maxim Kontsevich, and Anatoly Fomenko.
Source: University of Kentucky
Representations of p-adic groups, e.g., invertible matrices over the p-adic numbers, are an intensely studied area of mathematics that also plays a key role in the Langlands program and has applications to automorphic forms (generalizations of modular forms), among others. In my talk I will explain what I mean by p-adic groups and then I might survey the current state of the art of our understanding of the structure of the whole category of representations of p-adic groups, including recent and forthcoming results that relate the blocks of this category to depth-zero blocks of another p-adic group under minor tameness assumptions. Depth-zero representations correspond to representations of finite groups of Lie type and are much better understood than general representations of p-adic groups. Relating arbitrary blocks to depth-zero blocks therefore allows us to reduce many problems about representations of p-adic groups and the Langlands program to depth-zero representations, where the answer is either already known or easier to achieve.This reduction-to-depth-zero result has recently been obtained for representations with complex coefficients in two joint preprints with Jeffrey Alder, Manish Mishra and Kazuma Ohara. The case of representations with much more general coefficient rings is joint work in progress with Jean-François Dat. The techniques used in both cases are quite different, as I might sketch in my talk.
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\"Nonlocal Ordered Mean Curvature with Integrable Kernel\" by Animesh Biswas (8 - Analysis)
\"On I-Convergence, I-Limit Point and I-Cluster Point of Sequences of Bi-Complex Numbers\" by Shyamal Debnath (8 - Analysis)
\"On Nonsmooth Global Implicit Function Theorems for Locally Lipschitz Functions from Banach Spaces to Euclidean Spaces\" by Guy Degla (8 - Analysis)
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\"Fractional Maps of Generalized Beta Functions and Their Applications to Astrophysical Reaction Rates\" by Hussaini Joshua (8 - Analysis)
\"Directional Poincaré inequality on compact Lie groups\" by Andre Kowacs (8 - Analysis)
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\"Perturbation Ideals and Fredholm Theory in Banach Algebras\" by Tshikhudo Lukoto (8 - Analysis)
\"A Story-Based Introduction to Time Scale Calculus\" by Shekhar Singh Negi (8 - Analysis)
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\"Some fixed point theorems in strictly convex Menger PM-spaces\" by Rale Nikolic (8 - Analysis)
\"Directional Maximal Operators and Kakeya-Type Sets\" by Blanca Radillo-Murguia (8 - Analysis)
\"STABLE CLOSE-TO-CONVEXITY AND RADIUS OF FULL CONVEXITY FOR SENSE-PRESERVING HARMONIC MAPPINGS\" by Ankur Raj (8 - Analysis)
\"Proportional Calculus and Proportional Differential Equations: Theory and Applications\" by Mayuree Sompui (8 - Analysis)
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\"Oblique Dual Frame Completion in Euclidean Spaces: A Product Matrix Approach\" by Gino Angelo Velasco (8 - Analysis)
\"Construction of Mercedes-Benz Frames via QR Factorization\" by Long Wang (8 - Analysis)
\"Restriction and Kakeya maximal estimates in Four Dimensions\" by Yufei Zhan (8 - Analysis)
\"Weighted estimates for some class of quasilinear operators\" by Nazerke Zhangabergenova (8 - Analysis)
We survey the interplay between ergodic theory and additive combinatorics over the past few decades, tracing the path from foundational ideas to higher-order Fourier analysis and onward to its modern applications and the open questions that continue to shape the field.
\"Fröhlich-Spencer contours in Multidimensional Long-Range Ising Models\" by Rodrigo Bissacot (11 - Mathematical Physics)
\"Cohomological vertex algebras\" by Colton Griffin (11 - Mathematical Physics)
\"Topological Stability of Beltrami Fields as a Framework for Flavor Symmetry Alignment\" by Charles Grimm (11 - Mathematical Physics)
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\"The Resolvent Method in Complex Dynamics with applications to building a bridge between Schramm–Loewner Evolutions and Random Matrix Theory, and beyond\" by Vlad Margarint (12 - Probability)
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\"Equity Premium in a Semimartingale Market When Jump Amplitudes Follow an Arbitrary, Normal, Binomial and Gamma Distributions While Assuming Some Selected Utility Functions\" by George Mukupa (18 - Stochastic and Differential Modelling)
\"On the Concept of Digital Pathogens and Their Impact on 'Technopandemics'\" by Farai Nyabadza (18 - Stochastic and Differential Modelling)
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\"A Study of Overcompensatory Prey Growth on Discrete-Time Predator-Prey Model with Continuous and Seasonal Breeding\" by Narendra Pant (18 - Stochastic and Differential Modelling)
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\"Can we save the Tasmanian devil and restore ecosystem balance in Tasmania? \" by Megan Powell (18 - Stochastic and Differential Modelling)
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The American Mathematical Society and zbMATH Open will honor the many reviewers who share their expertise so that mathematicians, researchers, librarians, and others can navigate the increasingly complicated world of research in the mathematical sciences.
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Several problems in machine learning are naturally expressed as the design and analysis of time-evolving probability distributions. This includes sampling via diffusion methods, optimizing the weights of neural networks, and analyzing the evolution of token distributions across layers of large language models. While the targeted applications differ (samples, weights, tokens), their mathematical descriptions share a common structure. A key idea is to switch from the Eulerian representation of densities to their Lagrangian counterpart, through vector fields that advect particles. This dual view introduces challenges, notably the non-uniqueness of Lagrangian vector fields, but also opportunities to craft density evolutions and flows with favorable properties in terms of regularity, stability, and computational tractability. This survey presents an overview of these methods, with an emphasis on two complementary approaches: diffusion methods, which rely on stochastic interpolation processes and underpin modern generative AI, and optimal transport, which defines interpolation by minimizing displacement cost. We illustrate how both approaches appear in applications ranging from sampling and neural network optimization to modeling the dynamics of transformers in large language models.
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Film Directed by Josef Gatti
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We present some developments in the study of chaotic dynamics following the solution of a conjecture of Newhouse on the measures maximizing the entropy of smooth surface diffeomorphisms. We focus on strong positive recurrence, a generalization of the classical Anosov-Smale theory of uniform hyperbolicity which we introduced with Sylvain Crovisier and Omri Sarig. We will explain why this new property is general enough to be satisfied by all smooth surface diffeomorphisms with positive entropy. Then we will see how many quantitative properties such as exponential mixing or limit theorems for regular functions follow from it. We also present some open problems, including its abundance (or not) in higher dimensions.
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Film Directed by Ekaterina Eremenko
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Source: Discretization in Geometry and Dynamics
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"richTextDescription": "The Jacobian conjecture has been launched by O. Keller in 1939 and is still open until now, saying that a polynomial function $G$ from $\\mathbb{R}^n$ to itself for $n\\geq2$ having jacobian $det\\left(J_G\\right)$ equal to 1, is bijective. It is the 16th on the Smale's list of problems for the 21st century. We solve partially it when $n=2$ on the coordinate system $(x,y)$ with $G=(G_1,G_2)$ when $$G_1:=a_0+a_1x+l_1y+\\sum^m_{i=1}b_ixy^i+\\sum^m_{i=1}e_ix^2y^i+\\sum^m_{i=2}c_iy^i+\\sum^m_{i=2}f_ix^i$$$$G_2:=a_{-1}+r_1x+s_1y+\\sum^m_{i=1}k_ixy^i+\\sum^m_{i=1}w_ix^2y^i+\\sum^m_{i=2}t_iy^i+\\sum^m_{i=2}u_ix^i,$$where all coefficients of the polynomials are real. We define the degree of $G$ as $deg(G)=m$ for $m\\geq2$ and solve $det\\left(J_G\\right)=1$ by Maple: First, for $f_i=u_i=e_i=w_i=0$ for all $2\\leq i\\leq m$ when $e_1=w_1=0$ by solving $det\\left(J_G\\right)=1$ for $deg(G)=2m$ when $f_i=u_i=e_i=w_i=0$ for all $2\\leq i\\leq 2m$, $e_1=w_1=0$ and $b_i=c_i=k_i=t_i=0$ for all $m+1\\leq i\\leq 2m$. Then, we find that $G$ is injective, then $G$ is a bijection. Second, when $e_i=w_i=0$ for all $1\\leq i\\leq m$, we have $f_i=u_i=0$ for all $3\\leq i\\leq m$. Then, we have three cases to be solved in Maple up to the symmetry on $(x,y)$: the first is the one above which has already been solved, the second is:$$G_1:=a_0+a_1x+l_1y+\\sum^s_{i=2}c_iy^i$$$$G_2:=a_{-1}+r_1x+s_1y+\\sum^s_{i=1}k_ixy^i+\\sum^{2s}_{i=2}t_iy^i+\\sum^2_{i=2}u_ix^i,$$and the last is:$$G_1:=a_0+a_1x+l_1y+\\sum^{s}_{i=1}b_ixy^i+\\sum^{2s}_{i=2}c_iy^i+\\sum^2_{i=2}f_ix^i$$$$G_2:=a_{-1}+r_1x+s_1y+\\sum^s_{i=1}k_ixy^i+\\sum^{2s}_{i=2}t_iy^i+\\sum^2_{i=2}u_ix^i$$ for $s\\geq1$ and $2s\\leq m$. Let us use the following theorem, $G$ beying polynomial, $G$ is proper if and only if $G$ hasn't zero in the infinity. We solve $G_1(x,y)=0$ and $G_2(x,y)=0$ as polynomials of second degree in $x$, looking for zeros of $G$ in the infinity by Maple. Thus, We find that $G$ is proper. $G$ beying a local homeomorphism and proper, by the Hadamard theorem on local homeomorphism, $G$ is bijective. Third, we solve $det\\left(J_G\\right)=1$ in general form and we have $e_i=w_i=0$ for all $2\\leq i\\leq m$, we run again the Maple program with this data when $e_1\\neq0$ or $w_1\\neq0$, we find that $deg(G)\\leq4$. By Moh's result saying that if the usual degree of $G$ is less than 101, the Jacobian conjecture is true for $n=2$, we get $G$ as a bijection. We conclude by these results that $G$ verifies the Jacobian conjecture for $m\\geq2$.",
"plainTextDescription": "The Jacobian conjecture has been launched by O. Keller in 1939 and is still open until now, saying that a polynomial function $G$ from $\\mathbb{R}^n$ to itself for $n\\geq2$ having jacobian $det\\left(J_G\\right)$ equal to 1, is bijective. It is the 16th on the Smale's list of problems for the 21st century. We solve partially it when $n=2$ on the coordinate system $(x,y)$ with $G=(G_1,G_2)$ when $$G_1:=a_0+a_1x+l_1y+\\sum^m_{i=1}b_ixy^i+\\sum^m_{i=1}e_ix^2y^i+\\sum^m_{i=2}c_iy^i+\\sum^m_{i=2}f_ix^i$$$$G_2:=a_{-1}+r_1x+s_1y+\\sum^m_{i=1}k_ixy^i+\\sum^m_{i=1}w_ix^2y^i+\\sum^m_{i=2}t_iy^i+\\sum^m_{i=2}u_ix^i,$$where all coefficients of the polynomials are real. We define the degree of $G$ as $deg(G)=m$ for $m\\geq2$ and solve $det\\left(J_G\\right)=1$ by Maple: First, for $f_i=u_i=e_i=w_i=0$ for all $2\\leq i\\leq m$ when $e_1=w_1=0$ by solving $det\\left(J_G\\right)=1$ for $deg(G)=2m$ when $f_i=u_i=e_i=w_i=0$ for all $2\\leq i\\leq 2m$, $e_1=w_1=0$ and $b_i=c_i=k_i=t_i=0$ for all $m+1\\leq i\\leq 2m$. Then, we find that $G$ is injective, then $G$ is a bijection. Second, when $e_i=w_i=0$ for all $1\\leq i\\leq m$, we have $f_i=u_i=0$ for all $3\\leq i\\leq m$. Then, we have three cases to be solved in Maple up to the symmetry on $(x,y)$: the first is the one above which has already been solved, the second is:$$G_1:=a_0+a_1x+l_1y+\\sum^s_{i=2}c_iy^i$$$$G_2:=a_{-1}+r_1x+s_1y+\\sum^s_{i=1}k_ixy^i+\\sum^{2s}_{i=2}t_iy^i+\\sum^2_{i=2}u_ix^i,$$and the last is:$$G_1:=a_0+a_1x+l_1y+\\sum^{s}_{i=1}b_ixy^i+\\sum^{2s}_{i=2}c_iy^i+\\sum^2_{i=2}f_ix^i$$$$G_2:=a_{-1}+r_1x+s_1y+\\sum^s_{i=1}k_ixy^i+\\sum^{2s}_{i=2}t_iy^i+\\sum^2_{i=2}u_ix^i$$ for $s\\geq1$ and $2s\\leq m$. Let us use the following theorem, $G$ beying polynomial, $G$ is proper if and only if $G$ hasn't zero in the infinity. We solve $G_1(x,y)=0$ and $G_2(x,y)=0$ as polynomials of second degree in $x$, looking for zeros of $G$ in the infinity by Maple. Thus, We find that $G$ is proper. $G$ beying a local homeomorphism and proper, by the Hadamard theorem on local homeomorphism, $G$ is bijective. Third, we solve $det\\left(J_G\\right)=1$ in general form and we have $e_i=w_i=0$ for all $2\\leq i\\leq m$, we run again the Maple program with this data when $e_1\\neq0$ or $w_1\\neq0$, we find that $deg(G)\\leq4$. By Moh's result saying that if the usual degree of $G$ is less than 101, the Jacobian conjecture is true for $n=2$, we get $G$ as a bijection. We conclude by these results that $G$ verifies the Jacobian conjecture for $m\\geq2$.",
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As artificial intelligence becomes embedded in education, much discussion has focused on what students can produce with AI or how it can automate assessment and feedback. Yet mathematics is defined as much by process as by product. Its essence lies in conjecturing, reasoning, reflecting, and persisting through uncertainty. Drawing on research in the science of learning, this presentation explores what it means to keep the human at the centre of mathematical learning in an AI-mediated world. It highlights the importance of metacognitive awareness, emotional regulation, and the attitudes that sustain curiosity and persistence in the face of challenge.
Our research on mathematics anxiety shows how performance-oriented environments can undermine these processes, reducing confidence and willingness to explore. Learning to learn mathematics in an AI world means refocusing education on how students think, feel, and make sense of ideas, not only on what they can produce.
Usually, students learn mathematics and learn languages B,C,... separately. If they learn mathematics in their native language A then they will have difficulty understanding mathematical and technical texts in B because each language has peculiarities in difference between everyday and scientific terminology, denotation systems (for example, ‘obtuse angle’ is said ‘wide angle’; ‘round’ does not exist, different terms are used for ellipsoid with semi-axes a~b~c, with semi-axes a~b>>c, with semi-axes a>>b~c in Kyrgyz). If they learn mathematics in B then they have difficulty understanding because of insufficient knowledge of B. We propose to learn foundations of mathematics as constituent of natural language in its independent presentation. We participated in introducing a definition of independent computer presentation of an object (the user can master the object without reference to similar objects). Particularly, it means that the user is to be able to master foundations of the language by using corresponding software (with interactive actions and feedback) without any other language as a media. Hence, the only software is needed for presentation of any natural language regardless of native languages of users. The user thinks and counts in a learned language without translation in mind. To implement such software, definitions of ‘almost-closed or affectable objects’ (including both humans and computers), of ‘commands’ (low-energetic outer influences on affectable objects causing sufficiently various high-energetic reactions), of mathematical and computer models of notions of natural languages were introduced. A mathematical model of a notion consists of preliminaries list (if the notion is not primary); media description (objects presented as sets on display); permitted and prohibited relations between objects (overlapping, intersection, inclusion) and the user’s Drag-and-Drop actions (moving
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Dr. Emma LaPlace is an Assistant Professor of Mathematics at Albertus Magnus College in New Haven, Connecticut, where she also teaches Drama. Her research focuses on the intersection of mathematics and theater. Dr. LaPlace was a double-major in Mathematics and Drama during her undergraduate studies at Vassar College, and earned her PhD from Columbia University. Dr. LaPlace has acted professionally at theaters across Connecticut. Her recent published works can be seen in Mathematical Association of America Focus, and International Journal of Mathematical Education in Science and Technology. She has served as a math/theater consultant, and is currently collaborating with the Conference Board of the Mathematical Sciences for the 2026 Year of Math (you can find her monthly Math on Stage videos on theyearofmath.org). Her Instagram is @mathdramatics.
We survey some recent and in-progress structural and geometric tools for computing Fukaya categories of Liouville and Weinstein sectors and distinguished subcategories within them. Then we describe some applications and desired goals of this framework, including within mirror symmetry.
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After discovering the critical value of the local maximum in 1956, Lehmer formulated the assumption that the Hardy function could have a negative local maximum or a positive local minimum.
The paper proves the statement about the transformation of the zeros of the Hardy function, which doubts the Lehmer phenomenon:
I) the zeros of the Hardy function can be obtained by transforming the zeros of the function $\\cos\\theta(t)$;
II) all zeros of the Hardy function obtained by transformation are real;
III) the Hardy function has no other zeros except those obtained by transformation.
In the course of the proof, several expressions were obtained that had not previously been considered by other researchers of the Zeta function:
1) Summation of the Zeta function based on the properties of partial sums of the Dirichlet series to form an almost regular polygon on the complex plane;
2) Definition and summation of the generalized Hardy function as the real part of the Hardy function on any line parallel critical line;
3) A property of the generalized Hardy function is established, which makes it possible to associate its zeros with the zeros of the function $\\cos\\theta(t)$;
4) Based on the binomial series, an expression is obtained for the transformation of a generalized Hardy function between any two lines parallel to a critical line.It is shown that the real zeros of the functions obtained by the transformation of the generalized Hardy function form either a strictly decreasing or strictly increasing sequence.
The interval between the values $\\sigma=1/2$ and $\\sigma = \\hat\\alpha_\\lambda$ is divided into $\\mu_\\lambda$ intervals and it is shown by induction that the zeros of the generalized Hardy function on any line parallel critical line, including the most critical line, are real.
It is shown that the number of zeros of the Hardy function obtained by transformation from the function $\\cos\\theta(t)$ matches with the number of zeros $\\zeta(s)$ in the region of the critical strip with a height equal to the interval on which we calculated the number of zeros of the function $\\cos\\theta(t)$, therefore, the Hardy function has no other zeros in this interval.",
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We will discuss this rigidity phenomenon in several settings and present recent results, for example demonstrating rigidity for partially hyperbolic dynamical systems in higher-rank semisimple Lie groups of smooth diffeomorphisms of compact manifolds. The motor behind rigidity is the existence of symmetries, that is, commutation relations between dynamical systems. We will explain some of the key mechanisms arising from the interplay of symmetries, that lead to the smooth classification of the dynamics, meaning that up to a smooth change of coordinates, the dynamics is defined via algebraic transformations.
In this paper we study the frequentist properties of Bayesian approaches in linear high dimensional Hawkes processes in a sparse regime where the number of interaction functions acting on each component of the Hawkes process is much smaller than the dimension. We consider two types of loss function: the empirical L1 distance between the intensity functions of the process and the L1 norm on the parameters (background rates and interaction functions). Our results are the first results to control the L1 norm on the parameters under such a framework. They are also the first results to study Bayesian procedures in high dimensional Hawkes processes.
We show that any two same-genus, oriented, boundary parallel surfaces bounded by a non-split, alternating link into the 4-ball are smoothly isotopic fixing boundary. In other words, any same-genus Seifert surfaces for a non-split, alternating link become smoothly isotopic fixing boundary once their interiors are pushed into the 4-ball. We conclude that a smooth surface in $S^4$ obtained by gluing two Seifert surfaces for a non-split alternating link is always smoothly unknotted.
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This paper introduces new structures ${\\cal DV}$, ${\\cal FL}$ on a set $\\Xi$. It will be known as Diving structures and Floating structures. The pairs $(\\Xi, {\\cal DV})$, $(\\Xi, {\\cal FL})$ will be called Diving spaces and Floating spaces, respectively. These structures are not related to each other and are not related to any of the previous structures: Topology, Supra Topology, Infra Topology, Anti Topology, Generalized Structure, Weak Structure, Generalized Weak Structure, Minimal Structure, Ideal, Filter, Grill or Primal. We study some properties to characterize these new notions.
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This talk presents explicit constructions of automorphic forms on loop groups via the Weil representation and theta lifting. We review Eisenstein series on loop groups, including Garland's results and the entireness of cuspidal Eisenstein series. We then discuss the Weil representation of loop symplectic groups, the Siegel-Weil formula for loop groups, and the loop group generalization of the Rallis constant term formula for theta lifting, tower properties which yields a criterion for cuspidality and provides explicit cusp forms on loop groups. Finally, we present new explicit formulas for theta lifts from SL(2) to loop orthogonal groups and discuss their relation to Hecke eigenforms.
In statistics and machine learning, an algorithm that inputs training data and returns a fitted model is said to satisfy algorithmic stability if its output is not substantially altered by randomly resampling or removing a small number of data points from the training set. Algorithmic stability plays a crucial role in many results in statistics, particularly in the assumption-lean or distribution-free regime where we aim to avoid placing assumptions on the distribution of the data. At the same time, we may also want to certify that an algorithm is stable, or to construct an algorithm that is guaranteed to be stable, again in a distribution-free way if possible. This talk will highlight some results that span these different questions. Specifically, we will see how algorithmic stability allows for cross-validation to be used for distribution-free predictive inference. However, we will also see an impossibility result that limits our ability to certify that a black-box algorithm is stable without making assumptions. Fortunately, by using bagging (averaging over models fitted to repeated subsamples of the data), any black-box algorithm can be automatically guaranteed to be stable. In combination, these findings illustrate some of the benefits and challenges of the algorithmic stability framework in the distribution-free regime. The results presented in this talk are based on joint work with Emmanuel Candes, Aaditya Ramdas, Ryan Tibshirani, Jake Soloff, Rebecca Willett, Byol Kim, and Yuetian Luo.
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"description": "\"Pitchfork bifurcation and traveling waves for a planar ensemble of rigid filaments with repulsive interaction\" by Gervy Marie Angeles (10 - Partial Differential Equations)
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\"The nonlinear Schrödinger equation on metric graphs\" by Damien Galant (10 - Partial Differential Equations)
\"Traveling Band Solutions in Degenerate Chemotactic Systems: Existence, Stability, and Pattern Selection\" by Isanka Hevage (10 - Partial Differential Equations)
\"Minkowski-curvature equation under a Schwarzian constraint\" by Kuo-Chih Hung (10 - Partial Differential Equations)
\"Existence and Uniqueness of the Navier-Stokes Initial Value Problem in Infinite Space \" by Kulyash Kaliyeva (10 - Partial Differential Equations)
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\"Partially holomorphic solutions of higher order totally characteristic equations\" by Jose Ernie Lope (10 - Partial Differential Equations)
\"Effects of Stage-structure and Dispersal Mechanism on Species' Persistence\" by Maria Amarakristi Onyido (10 - Partial Differential Equations)
\"Global dynamics of solitons coupled to radiation for critical wave maps and nonlinear wave equations\" by Mohandas Pillai (10 - Partial Differential Equations)
\"New Analytical Soliton Solutions and Dynamical Analysis of a Double-Stranded DNA Model\" by Md Nurul Raihen (10 - Partial Differential Equations)
\"On Hardy Inequalities with Homogeneous Weights\" by Subhajit Roy (10 - Partial Differential Equations)
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\"AI-Driven Data Augmentation and Sensitivity Analysis of Radiative Bödewadt Ternary Nanofluid Flow over a Porous Rotating Disk with Multiple Slips\" by Shahirah Abu Bakar (11 - Mathematical Physics)
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\"On the Matrix Negative Order Korteweg-de Vries Equation - the Commutative Case\" by Aygul Babadjanova (11 - Mathematical Physics)
\"Transport Boundary Value Problems for the Klein-Gordon Equation and Their Solution \" by Aigulim Bayegizova (11 - Mathematical Physics)
\"Mixed Physical Informed Neural Networks in Bio-Fluid Mechanics: Ureter Applications\" by Kh Mekheimer (11 - Mathematical Physics)
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\"Bit Complexity of Polynomial GCD on Sparse Representation\" by Xiaoshan Gao (14 - Mathematics of Computer Science)
\"Evolutionary Game Theory (EGT) Provides a Rigorous Mathematical Paradigm for Automating Optimal Large Language Model (LLM) Selection\" by Prasad Kothari (14 - Mathematics of Computer Science)
\"Detection of Malicious Images Generated by Large Language Models Using Graph Neural Networks and Feature-Based Representations\" by Mohammed Serrhini (14 - Mathematics of Computer Science)
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\"Image Encryption Based On Newly Designed Chaotic Map\" by Kritika Gupta (17 - Statistics, Machine Learning, Image and Signal Processing)
\"Predictive Models for Breast Cancer Brain Metastasis: An Integration of Neuroimaging and Genomics Data for Better Clinical Practice\" by Chipo Zidana (17 - Statistics, Machine Learning, Image and Signal Processing)
The conjectures of Gromov–Lawson and Gromov predict obstructions to the existence of Riemannian metrics of positive scalar curvature on closed manifolds in terms of their asphericity and large-scale geometry, respectively. In this talk, I will address these conjectures for Kähler metrics on smooth projective varieties. In detail, I will show that a smooth projective variety that is aspherical (or, more generally, whose universal cover has maximum macroscopic dimension) cannot support a Kähler metric of positive scalar curvature. The statement will be refined for totally non-spin manifolds and complex projective surfaces. The proofs of these results draw new connections between the theories of minimal models, positivity in complex algebraic geometry, and macroscopic dimensions. This talk is based on joint work with Luca F. Di Cerbo and Alexander Dranishnikov.
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\"Determining Wavenumbers for Hall and Electron Magnetohydrodynamics\" by Hassan Babaei (10 - Partial Differential Equations)
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\"A Constructible Conductivity Cloak via Homogenisation\" by Eleanor Gemida (10 - Partial Differential Equations)
\"On an Algorithm for Finding Solutions of Initial–Boundary Value Problem for Functional–Hyperbolic Equation with Distributed Parameters\" by Narkesh Iskakova (10 - Partial Differential Equations)
\"A Topological Derivative-Based Method to Image Inhomogeneities in an Acoustic Waveguide\" by Umid Karimov (10 - Partial Differential Equations)
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\"Geometric Rigidity and Unstable Set Decomposition of Normally Hyperbolic Frozen Waves\" by Jihoon Lee (10 - Partial Differential Equations)
\"A coupled PDE–ODE system with boundary interaction arising in heat transfer\" by Le Duc Nhien (10 - Partial Differential Equations)
\"Global Boundedness and Pattern Formation in a Flux-Limited Keller–Segel System with Logistic Growth\" by Ruiliang Li (10 - Partial Differential Equations)
\"Regime Dependent Infection Propagation Fronts in an SIS Model.\" by Vahagn Manukian (10 - Partial Differential Equations)
\"A Nash Stratification Inequality and Global Regularity for a Chemotaxis-Fluid System on General 2D Domains\" by Naji Sarsam (10 - Partial Differential Equations)
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\"Discrete Wave Turbulence of a Coupled System of Quintic Schrödinger Equations\" by Shayan Zahedi (10 - Partial Differential Equations)
Moderators:
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Join us in Hall E for a family-friendly Math Festival open to the public. This interactive celebration of mathematics will feature hands-on activities, engaging talks, games and art designed to inspire curiosity and showcase the beauty and creativity of math for all ages. Discover how mathematics connects to everyday life, science, and culture while experiencing the excitement of one of the world’s largest gatherings of mathematicians.
MathHappens Activity Area
- Multi-station interactive math playground featuring puzzles, tiles, and tactile models that encourage exploration, pattern recognition, and informal learning through hands-on discovery.
Maze Mat / Twist-n-Roll / Ring of Fire
- Dynamic large-scale interactive math installations including floor-based mazes, tactile exhibits, and collaborative builds designed for full-body engagement and high visitor throughput.
Probability Power / Clothesline of Chance
- Interactive game-show style probability experience where participants engage in live challenges (coin flipping + probability ranking) to build intuition around chance and real-world likelihood (close line).
Interactive Math Festival
- Large-scale hands-on math festival environment featuring multiple table-based activities designed to spark curiosity, collaboration, and joyful problem-solving for K–8 audiences.
Are We There Yet? An Exploration of Distance
- Immersive multi-model math exploration combining physical builds, interactive puzzles, and VR to demonstrate different concepts of distance and geometry across mathematical systems.
Math Card Game Exhibit
- Interactive math card game experience connecting middle school math concepts to real-world scenarios through collaborative, play-based problem solving.
Sierpinski Simplices
- Collaborative fractal-building activity where participants construct a large Sierpinski tetrahedron through hands-on assembly, illustrating patterns, scaling, and mathematical structure.
Ideal fluid flows are dynamical rearrangements of space that minimize kinetic energy. Such flows, which solve the Euler equations, exhibit a wide range of interesting phenomena. We will give an overview of many of these phenomena, which have been rigorously established by many authors in recent years, and then focus mainly on questions related to steady solutions and finite-time singularities.
Many complex systems can be modeled by very large graphs. Such graphs exhibit robustness, randomness, dynamic behavior, and distinctive structural features, while at the same time sharing several fundamental properties. A central issue in the study of complex systems is the partitioning of a population into communities, where each community exhibits common behavior and shared interests. Numerous research efforts have proposed and developed a variety of methodological approaches to address this problem.In this presentation, we will discuss models for large graphs and present algorithms for community detection, both with and without overlapping communities, based on random walk theory.
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Simons Laufer Mathematical Sciences Institute and Johnny Houston, NAM that traces the evolution of a culture of Black scholars, scientists and educators. The film follows the stories of prominent pioneers, the challenges they faced and their triumphs as they are reflected in the success and contributions of today's productive Black mathematicians who followed them.
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The subject of upper-triangular totally positive Toeplitz matrices turns out to be a rich one, relating in the infinite case to the infinite symmetric group and its representations (classical theory), and in the finite case to flag varieties and their quantum cohomology rings (modern). We describe the asymptotics of the modern theory and tropicalise both to uncover a third relation, to the parametrisation of Lusztig's canonical basis.
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We report on certain results and open questions related to the dynamics of foliations on algebraic compact complex surfaces, with a particular emphasis on the geography of the stability/bifurcation loci in their moduli spaces.
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\\documentclass[11pt]{article}\\usepackage[utf8]{inputenc}\\usepackage[T1]{fontenc}\\usepackage{geometry}\\geometry{margin=1in}\\title{\\textbf{Recent Results on Sampling Type Series and Applications to Image Processing}}\\author{Tuncer Acar\\\\\\small Selcuk University, Faculty of Science\\\\\\small Department of Mathematics\\\\\\small 42003, Selcuklu, Konya, T\\\"urkiye}\\date{}\\begin{document}\\maketitle\\begin{abstract}In this talk, we present several recent developments concerning sampling type series and their approximation properties in various function spaces. Sampling type series constitute an important class of approximation operators, playing a fundamental role in approximation theory, harmonic analysis, and signal reconstruction. In recent years, significant progress has been made in understanding their convergence behavior and rate of approximation under different structural assumptions.A particular emphasis will be placed on the study of sampling type series in weighted function spaces. We discuss how the presence of suitable weight functions influences the approximation order, smoothness preservation, and error estimates of these operators. Connections with modulus of continuity, quantitative estimates, and embedding properties of weighted spaces will be highlighted, illustrating the advantages of working within this more general framework.In the second part of the talk, we focus on applications of sampling type series to image processing. We demonstrate how the theoretical results can be effectively employed in practical problems such as image reconstruction, denoising, and resolution enhancement. Several examples will be discussed to show how sampling based approximation schemes provide efficient and robust tools for processing digital images. The aim of this presentation is to bridge the gap between abstract approximation theory and concrete applications in image and signal processing.\\end{abstract}\\end{document}
Log concavity is an important feature of many functions and discrete sequences appearing across mathematics, including combinatorics, algebraic geometry, convex analysis, and optimization. In this talk I will survey recent developments in our understanding of functional log concavity with a focus on applications to combinatorial inequalities and algorithms for approximate counting and sampling. At the heart of this story are rich classes of multivariate generating polynomials that give rise to discrete probability distributions that can be approximately sampled efficiently using Markov chains. The basis-generating polynomial of a matroid is a fundamental example. We will explore applications to matroids and extensions to other combinatorial structures.
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\"Collapsing of Minimality Conditions in Divisible Ordered Abelian Groups\" by Jacob Stern (1 - Logic)
\"Gotzmann thresholds of monomials: a general method and its application\" by Vittoria Bonanzinga (2 - Algebra)
\"On a Finite-Iteration Method for Solving SLAE\" by Roman Filippov (2 - Algebra)
\"Nilpotent associative algebras\" by Ikboljon Karimjanov (2 - Algebra)
\"Sets of lengths of integer-valued polynomials on prime ideals\" by Sarah Nakato (2 - Algebra)
\"On Complete Integral Closedness, Skew-Injectivity, and π-Injectivity of Modules\" by Muamar Musa Nurwigantara (2 - Algebra)
\"Representations and Cohomologies of the Alternating Group of Degree 4\" by Andriiana Plakosh (2 - Algebra)
\"Enumerating Log Rational Curves on $\\mathbb{P}_{\\mathbb{P}^r}(\\mathcal{O}^s\\oplus \\mathcal{O}(-a))$\" by Naufil Sakran (2 - Algebra)
\"Weitzenböck Remainder Spectrum on Rational Omogeneous Varieties\" by Lucas Almeida (5 - Geometry)
\"Study of Clairaut Anti-Invariant Riemannian Maps from Sasakian Manifolds\" by Garima Goel (5 - Geometry)
\"Sharp Minkowski Type Inequality in Cartan-Hadamard 3-Spaces\" by Fang Hong (5 - Geometry)
\"A Study of Lightlike Submanifolds of Indefinite Statistical Manifolds\" by Varun Jain (5 - Geometry)
\"Compact Holonomy and Riemannian Metrizability in Finsler Geometry\" by Sendrasoa Laurence Lantonirina (5 - Geometry)
\"Infinitesimal Bending of Dual Curves and Its Geometric Characterizations\" by Marija Najdanović (5 - Geometry)
\"Quadratic Killing tensors on Symmetric Spaces\" by An Ky Duy Nguyen (5 - Geometry)
\"On the dimension of the nullity space of the curvature tensor on Riemannian manifold\" by Princy Randriambololondrantomalala (5 - Geometry)
\"Study of Holomorphic Riemannian Maps from Nearly Kaehler Manifolds\" by Rashmi Sachdeva (5 - Geometry)
\"On the Roter type of Generalised Wintgen Ideal Legendrian Submanifolds\" by Aleksandar Šebeković (5 - Geometry)
\"GEOMETRY OF POINT PARTICLES. SYMBOLIC COMPUTER VERIFICATION OF THE ATIYAH’S CONJECTURE FOR FIVE POINTS IN THE EUCLIDEAN PLANE\" by Dragutin Svrtan (5 - Geometry)
\"Bonnet--Myers-type Theorems via Bakry--\\'{E}mery Ricci Curvature of Exponential Decays\" by Homare Tadano (5 - Geometry)
\"Area-minimizing capillary cones\" by Raphael Tsiamis (5 - Geometry)
\"On Shape and Energies of Geometric Objects \" by Ljubica Velimirovic (5 - Geometry)
\"Graph Manifolds with Positive Artinian Presentations\" by Lorena Armas-Sanabria (6 - Topology)
\"The Chordal Distance Tr+[@[Abstract Title - Plain Text]]sform of Geometric Loops and its Persistent Homology\" by James Binnie (6 - Topology)
\"On Projective and Flat Persistence Modules\" by Giriraj Ghosh (6 - Topology)
\"Corank-One Orthosymplectic Reduction Superalgebras\" by Marcus McLaurin (7 - Lie Theory and Generalizations)
We study the small-time local controllability, in the vicinity of an equilibrium, of a nonlinear scalar-input system. A natural strategy consists in proving the controllability of the linearized system at the equilibrium and conclude with a local inversion argument. When this linearized system is not controllable, it is necessary to study the quadratic term. In this article, we link several recent results on this subject. We also propose a unified methodology to prove quadratic obstructions to local controllability, that relies on systematic drift estimates.
For finite-dimensional control systems, quadratic terms only generate obstructions to controllability: they introduce coercive drifts in the dynamics, quantified by negative integer Sobolev norms of the control, linked to Lie brackets.
In infinite dimension, the same obstructions persist, but two new behaviors occur. First, quadratic obstructions can be due to drifts quantified by other norms (for instance fractional Sobolev norms); their geometric interpretation is challenging. Second, and more strikingly, small-time local controllability can sometimes be recovered from the quadratic expansion.
The tools developed for these studies are also used to understand the influence of higher order terms on the small-time local controllability, for single or multi-input systems, and in other research areas.
We develop a mathematical framework that interprets Transformer attention as an interacting particle system and studies its continuum (mean-field) limits. By idealizing attention on the sphere, we connect Transformer dynamics to Wasserstein gradient flows, synchronization models (Kuramoto), and mean-shift clustering. Central to our results is a global clustering phenomenon whereby tokens cluster asymptotically after long metastable states where they are arranged into multiple clusters. We further analyze a tractable equiangular reduction to obtain exact clustering rates, show how commonly used normalization schemes alter contraction speeds, and identify a phase transition for long-context attention. The results highlight both the mechanisms that drive representation collapse and the regimes that preserve expressive, multi-cluster structure in deep attention architectures.
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\"On a Finite-Iteration Method for Solving SLAE\" by Roman Filippov (2 - Algebra)
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\"Study of Clairaut Anti-Invariant Riemannian Maps from Sasakian Manifolds\" by Garima Goel (5 - Geometry)
\"Sharp Minkowski Type Inequality in Cartan-Hadamard 3-Spaces\" by Fang Hong (5 - Geometry)
\"A Study of Lightlike Submanifolds of Indefinite Statistical Manifolds\" by Varun Jain (5 - Geometry)
\"Compact Holonomy and Riemannian Metrizability in Finsler Geometry\" by Sendrasoa Laurence Lantonirina (5 - Geometry)
\"Infinitesimal Bending of Dual Curves and Its Geometric Characterizations\" by Marija Najdanović (5 - Geometry)
\"Quadratic Killing tensors on Symmetric Spaces\" by An Ky Duy Nguyen (5 - Geometry)
\"On the dimension of the nullity space of the curvature tensor on Riemannian manifold\" by Princy Randriambololondrantomalala (5 - Geometry)
\"Study of Holomorphic Riemannian Maps from Nearly Kaehler Manifolds\" by Rashmi Sachdeva (5 - Geometry)
\"On the Roter type of Generalised Wintgen Ideal Legendrian Submanifolds\" by Aleksandar Šebeković (5 - Geometry)
\"GEOMETRY OF POINT PARTICLES. SYMBOLIC COMPUTER VERIFICATION OF THE ATIYAH’S CONJECTURE FOR FIVE POINTS IN THE EUCLIDEAN PLANE\" by Dragutin Svrtan (5 - Geometry)
\"Bonnet--Myers-type Theorems via Bakry--\\'{E}mery Ricci Curvature of Exponential Decays\" by Homare Tadano (5 - Geometry)
\"Area-minimizing capillary cones\" by Raphael Tsiamis (5 - Geometry)
\"On Shape and Energies of Geometric Objects \" by Ljubica Velimirovic (5 - Geometry)
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\"The Chordal Distance Tr+[@[Abstract Title - Plain Text]]sform of Geometric Loops and its Persistent Homology\" by James Binnie (6 - Topology)
\"On Projective and Flat Persistence Modules\" by Giriraj Ghosh (6 - Topology)
\"Corank-One Orthosymplectic Reduction Superalgebras\" by Marcus McLaurin (7 - Lie Theory and Generalizations)
In this talk we explain an approach to the study of smooth manifolds which compares them to presheaves on a category of discs, also known as embedding calculus. We highlight recent work that shows this approach has many desirable properties, as well as recent applications demonstrating its strength
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Tensors are higher-dimensional generalisations of matrices, and likewise the main notion of complexity on matrices - the rank - may be extended to tensors. For a long time the main such extension that was considered was the tensor rank. Throughout the past decade however, new notions have arisen. For instance, the slice rank originated in a reformulation by Tao in 2016 of the underlying tool in the breakthrough papers of Croot-Lev-Pach and Ellenberg-Gijswijt (both published in the Annals of Mathematics) on the cap-set problem. The partition rank was then defined one year later by Naslund in a similar context, and several other ranks have blossomed since then. It has now become clear that there is no single canonical notion of rank on tensors, and that the most useful notion instead depends on the application at hand.
In sharp contrast with the matrix case, the properties of the ranks of tensors are still poorly understood. This is largely due to the lack of tools leading to lower or upper bounds on these ranks. We will present several basic properties of the ranks of tensors, including suitable generalisations of the following two facts: that a rank-$k$ matrix must contain a $k$ by $k$ submatrix, and that a matrix has only one minimal-length decomposition up to a change of basis. As in many situations aimed at generalising a property of the rank of matrices to the ranks of tensors, the naive extension of the original property fails in a major way, yet still admits a rectification which is simultaneously not too complicated to state and in a spirit that is very close to that of the original property from the matrix case.
Abstract Anosov geodesic flows are among the simplest mathematical models of deterministic chaos. We explain how, quite unexpectedly, quantum dynamics emerges from purely classical correlation functions. The underlying mechanism is the discrete Pollicott–Ruelle spectrum of the geodesic flow, revealed through microlocal analysis. This spectrum naturally arranges into vertical bands; when the rightmost band is separated from the rest by a gap, it governs an effective dynamics that mirrors quantum evolution.
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The music of J. S. Bach has influenced composers more than that of perhaps any other figure. His Trio Sonatas, in particular, offer some of the clearest insights into his pedagogy and have challenged generations of organists. For these reasons, they may also provide a uniquely powerful window into the structure of Bach’s music, and even into tonal music more broadly.
This talk will describe a collaborative project with the University of Michigan Organ Department to create high-precision digital recordings of these works, performed by students and faculty at varying skill levels. Using these digitization’s, together with direct representations of the musical scores, we investigate how music may be encoded in the mind.
Results challenge prevailing mathematical theories of music representation and reveal unexpected structural patterns in Bach’s compositions that invite further exploration. We also show how mathematical models of auditory processing in the brain can suggest new principles of musical composition.
Please note, as part of this experience, there will be an organ performance at Cathedral Basilica following the session (5:30 PM - 6:30 PM).
Click here to learn more about this session.
H. Furstenberg and B. Weiss first applied dynamical systems (topological dynamics) in Ramsey Theory, starting the extremely fruitful use of ergodic methods in combinatorics, which has provided many fundamental results over the years. One of the reasons why these methods have been so successful is because, in many cases, dynamical descriptions of Ramsey-theoretical problems are simpler than the algebraic or combinatorial ones; in other cases, the dynamical notions that arise from the study of combinatorial problems are interesting enough to be studied for themselves. Later, starting with the work of V. Bergelson and N. Hindman, several ergodic notions found an equivalent characterization in terms of special kinds of ultrafilters: for example, central sets where related to minimimal idempotents. In recent years, several papers have faced the problem of localizing known dynamical notions and results: for example, dynamical and combinatorial results near $0$ and near an idempotent. Patra studied the interplay between algebra and dynamics near zero and it has been extended to near idempotents. In 2009, O.Shuungula, Y. Zelenyuk, and Y. Zelenyuk introduced the notion of largeness along a filter which generalizes the notions of largeness near $0$ and near an idempotent and many othere notions of largeness.In this present work, we want to explore a setting that unifies and extends all those that have been developed so far, namely the notion of dynamics along a filter. We show that many classical definitions and properties of notions of large sets can be extended to dynamics along a filter. We study some basic properties of $\\mathcal{F}$-syndetic, piecewise $\\mathcal{F}$-syndetic, collectionwise $\\mathcal{F}$-piecewise syndetic, $\\mathcal{F}$-quasi central and $\\mathcal{F}$-central sets and their relations with $\\mathcal{F}$-uniformly recurrent points and ultrafilters. we provide some applications of our results to the partition regularity of nonlinear Diophantine equations along filters.
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L-functions are generalizations of the Riemann zeta function. Their analytic properties control the asymptotic behavior of prime numbers in various refined senses. Conjecturally, every L-function is a \"standard L-function\" arising from an automorphic form. A problem of recurring interest, with widespread applications, has been to establish nontrivial bounds for L-functions. I will survey some recent results addressing this problem. The proofs involve the analysis of integrals of automorphic forms, approached through the lens of representation theory. I will emphasize the role played by the orbit method, developed in a quantitative form along the lines of microlocal analysis, as well as inputs from the theory of homogeneous dynamics and effective equidistribution.
In many real-world scenarios, such as limited-view X-ray computed tomography (LVCT), the underlying signal possesses special properties, like nonnegativity, component-wise sparsity and group sparsity. This motivates one to develop an optimization model (and its solver) that takes into account the needed structural constraints. In this setting, one seeks to recover an unknown signal from an underdetermined linear system with highly ill-conditioned sensing operators, where classical sparse recovery assumptions are often violated. Driven by the potential of stated models for their applicability, we investigate a class of nonnegative group-sparse optimization problems arising in large-scale inverse problems and assuming the form \\[\\min_{\\mathbf{x} \\in \\mathbb{R}^n} \\;\\biggl[ \\mathcal{D}(\\mathcal{T}\\mathbf{x}, \\mathbf{b})+ \\lambda_1 \\Phi(\\mathbf{x})+ \\lambda_2 \\mathcal{G}(\\mathbf{x})+ \\mathcal{I}_{\\mathbb{R}^n_+}(\\mathbf{x}) \\biggl],\\]where $\\mathcal{T} \\in \\mathbb{R}^{n \\times m}$ is the sensing operator, $\\mathcal{D}$ is the data-fidelity term, and $\\mathbf{x}$ is the signal to be reconstructed. Here $\\mathcal{I}_{\\mathbb{R}^n_+}$ enforces component-wise nonnegativity, $\\Phi$ promotes sparsity, and $\\mathcal{G}$ enforces group sparsity. We employ a nonconvex transformed sparsity penalty of the form\\[\\Phi(\\mathbf{x}) = \\sum_{j=1}^n \\phi_a(w_j x_j),\\qquad\\phi_a(s) = \\frac{(a+1)|s|}{a+|s|},\\]which interpolates between $\\ell_0$ and $\\ell_1$ regularization as the parameter $a$ varies. It may be stated that group sparsity is imposed through penalties acting on grouped components of $\\mathbf{x}$, which make the problem constrained, nonsmooth and nonconvex. We propose a proximal iterative scheme to solve the afore-stated optimization problem along with convergence guarantees. We also want to deploy our proposed solver towards reconstructing images in an LVCT task.
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Long before combinatorics was recognized as a formal branch of mathematics, its principles were alive and flourishing in the cultural and intellectual life of the Indian subcontinent. Rooted in the systematic study of Sanskrit prosody (chandas), combinatorial procedures and techniques first emerged around 200 BCE in the Chandaḥsūtra of the Sanskrit prosodist Piṅgala. From these foundations, rules governing combinations and permutations gradually found expression in music and dramatic arts, visual art and architecture, medicine and pharmacology, and even divinatory practices. Yet their assimilation into more specialised mathematical spheres unfolded over a much longer period.The earliest evidence we have for the uptake of combinatorial rules in the mathematical sciences is a short chapter tucked away towards the end of a long and technical work on mathematical astronomy, the seventh century Brāhmasphuṭasiddhānta of Brahmagupta. Its inclusion appears somewhat eclectic relative to the work's primary purpose, and its highly terse nature has meant much of its technical content remained obscure to later authors. Despite this, the chapter caught the notice of the eleventh-century Persian polymath al-Bīrūnī whose exposition remained a key source of insight into the text until very recently. We investigate why this chapter has eluded scholars for so long and how, with the discovery of new source material, we are now in a better position to shed light on its mathematical content.
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Since its introduction by Richard Hamilton in 1982, the Ricci flow has become a fundamental tool in geometry and topology. From the point of view of PDE, the Ricci flow is a system of nonlinear parabolic equations. It can be viewed as the heat equation analogue of the Einstein equations in general relativity. The central problem is to understand singularity formation. In other words, what does the geometry look like at points where the curvature is large? In a spectacular breakthrough in 2002, Perelman achieved a qualitative understanding of singularity formation in dimension 3; this is sufficient for topological conclusions. In this lecture, we will discuss more recent developments which have led to a complete classification of singularity models in dimension 3.
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"description": "\"Pitchfork bifurcation and traveling waves for a planar ensemble of rigid filaments with repulsive interaction\" by Gervy Marie Angeles (10 - Partial Differential Equations)
\"On the existence of source-solutions to the multidimensional Burgers equation\" by JOÃO FERNANDO DA CUNHA NARIYOSHI (10 - Partial Differential Equations)
\"The nonlinear Schrödinger equation on metric graphs\" by Damien Galant (10 - Partial Differential Equations)
\"Traveling Band Solutions in Degenerate Chemotactic Systems: Existence, Stability, and Pattern Selection\" by Isanka Hevage (10 - Partial Differential Equations)
\"Minkowski-curvature equation under a Schwarzian constraint\" by Kuo-Chih Hung (10 - Partial Differential Equations)
\"Existence and Uniqueness of the Navier-Stokes Initial Value Problem in Infinite Space \" by Kulyash Kaliyeva (10 - Partial Differential Equations)
\"Initial-boundary value problems for Navier-Stokes-Voigt equations with power-law nonlinearity\" by Khonatbek Khompysh (10 - Partial Differential Equations)
\"Partially holomorphic solutions of higher order totally characteristic equations\" by Jose Ernie Lope (10 - Partial Differential Equations)
\"Effects of Stage-structure and Dispersal Mechanism on Species' Persistence\" by Maria Amarakristi Onyido (10 - Partial Differential Equations)
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\"On Hardy Inequalities with Homogeneous Weights\" by Subhajit Roy (10 - Partial Differential Equations)
\"On the asymptotics of attractors of the Ginzburg-Landau complex equation in a perforated domain with an oscillating boundary: Supercritical case\" by Altyn Toleubay (10 - Partial Differential Equations)
\"Using Differential-Equation-Based Methods to Automate Microscopy Segmentation in Developmental Biology\" by Markjoe Uba (10 - Partial Differential Equations)
\"AI-Driven Data Augmentation and Sensitivity Analysis of Radiative Bödewadt Ternary Nanofluid Flow over a Porous Rotating Disk with Multiple Slips\" by Shahirah Abu Bakar (11 - Mathematical Physics)
\"Electrogravimagnetic Field of a Toroidal Resonator with Biquaternion Representation of Currents\" by Bakhyt Alipova (11 - Mathematical Physics)
\"On the Matrix Negative Order Korteweg-de Vries Equation - the Commutative Case\" by Aygul Babadjanova (11 - Mathematical Physics)
\"Transport Boundary Value Problems for the Klein-Gordon Equation and Their Solution \" by Aigulim Bayegizova (11 - Mathematical Physics)
\"Mixed Physical Informed Neural Networks in Bio-Fluid Mechanics: Ureter Applications\" by Kh Mekheimer (11 - Mathematical Physics)
\"Enhancing Heat Transfer Using GO–MoS₂/Glycerine Hybrid Nanofluid under Slip Conditions on a Riga Plate\" by Nor Ain Azeany Mohd Nasir (11 - Mathematical Physics)
\"Magnetohydrodynamics Ternary Hybrid Nanofluid Flow Over a Permeable Moving Surface\" by Nur Syahirah Wahid (11 - Mathematical Physics)
\"Coordinate-Wise Elephant Random Walk\" by Denisse Escobar Parra (12 - Probability)
\"Stability Criteria for Rough Systems\" by Thanh Hong Phan (12 - Probability)
\"Boundary Value Problem with Parameter for Impulsive Integro-Differential Equation under Integral Constraints\" by Elmira Bakirova (14 - Mathematics of Computer Science)
\"Bit Complexity of Polynomial GCD on Sparse Representation\" by Xiaoshan Gao (14 - Mathematics of Computer Science)
\"Evolutionary Game Theory (EGT) Provides a Rigorous Mathematical Paradigm for Automating Optimal Large Language Model (LLM) Selection\" by Prasad Kothari (14 - Mathematics of Computer Science)
\"Detection of Malicious Images Generated by Large Language Models Using Graph Neural Networks and Feature-Based Representations\" by Mohammed Serrhini (14 - Mathematics of Computer Science)
\"Multivariate Information Measures: A Copula-Based Approach\" by Mohd Arshad (17 - Statistics, Machine Learning, Image and Signal Processing)
\"Image Encryption Based On Newly Designed Chaotic Map\" by Kritika Gupta (17 - Statistics, Machine Learning, Image and Signal Processing)
\"Predictive Models for Breast Cancer Brain Metastasis: An Integration of Neuroimaging and Genomics Data for Better Clinical Practice\" by Chipo Zidana (17 - Statistics, Machine Learning, Image and Signal Processing)
My goal in this session is to introduce the work done with bilingual (Spanish and English) students exploring, animating, and expressing mathematical concepts. The expressions and concepts that we have experienced in the bilingual classroom have helped us note that wonder as much as languaging are essential in the process of embodying mathematical concepts and feeling our connections to them and ourselves. Furthermore, in this process, I will conceptualize how the assemblages formed among students, objects, adults, and expressions—embedded in the physical and discursive animation of mathematical concepts—move through a translanguaging corriente or stream, which is nurtured through a mutual noticing and being with each other in the here and now. The sharing of our experiences facilitating and doing this work will be used as a platform to engage the participants in sharing their expressions on how this approach resonates with them and their contexts.
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"description": "Homotopy theory studies generalizations of commutative rings, called ring spectra, in which addition and multiplication are not necessarily strictly associative or commutative. Instead, addition and multiplication are required to be associative and commutative only up to canonical isomorphism, in the same sense that the set {a,b} is in bijection with, but not equal to, the set {b,a}. I will describe a program for generalizing cohomological invariants of rings and schemes to invariants of ring spectra and spectral schemes. Perhaps surprisingly, understanding these cohomological invariants plays an essential role in a modern accounting of the homotopy groups of spheres (as reflected in the disproof of Ravenel's Telescope Conjecture).
Finding and Defining Success in Mathematics: Pathways and Measures
Mathematics has often emphasized a narrow vision of what a successful career can look like. This panel expands that horizon by celebrating the many dynamic ways success can emerge across research, leadership, industry, and public engagement. Bringing together diverse experiences, perspectives, and insights, the discussion will explore how mathematicians navigate, shape, and define success along different professional pathways.
We warmly invite the entire mathematical community to join this conversation, reflect together, and imagine even more paths forward. Our hope is to inspire broad and inclusive understandings of achievement and impact across our field.
This panel is jointly organized by the Association for Women in Mathematics (AWM) and the IMU Committee for Women in Mathematics (CWM). Co-organizers include Carolina Araujo, Hélène Barcelo, Raegan Higgins, Lakeshia Legette Jones, Darla Kremer and Elaine Pimentel.
Panelists:
- Annalisa Crannell, Franklin & Marshall College
- Fern Hunt, National Institute of Standards and Technology
- Emily Riehl, Johns Hopkins University
- Shelby Wilson, Johns Hopkins University
Moderators:
Carolina Araujo, Instituto Nacional de Matemática Pura e Aplicada
- Darla Kremer, Association for Women in Mathematics
\"Fröhlich-Spencer contours in Multidimensional Long-Range Ising Models\" by Rodrigo Bissacot (11 - Mathematical Physics)
\"Cohomological vertex algebras\" by Colton Griffin (11 - Mathematical Physics)
\"Topological Stability of Beltrami Fields as a Framework for Flavor Symmetry Alignment\" by Charles Grimm (11 - Mathematical Physics)
\"Regularisation by noise of quasilinear partial differential equations\" by Antoine Marie Bogso (12 - Probability)
\"Statistical Geometrization: A Unified Measure-Theoretic and Probabilistic Resolution to the Riemann Hypothesis\" by Kemal Gursoy (12 - Probability)
\"Uniqueness of Invariant Measures for Stochastic Damped Anisotropic Navier–Stokes Equations on the Full Plane\" by Siyu Liang (12 - Probability)
\"LDP FOR TENSOR FORMS\" by Reihaneh Malekian (12 - Probability)
\"The Resolvent Method in Complex Dynamics with applications to building a bridge between Schramm–Loewner Evolutions and Random Matrix Theory, and beyond\" by Vlad Margarint (12 - Probability)
\"Multi-component matching queues with abandonment and buffers : Fluid, diffusion limit and large deviations\" by Souvik Ray (12 - Probability)
\"Lower deviations for critical branching processes with immigration\" by Sadillo Sharipov (12 - Probability)
\"A Dynamical Approach to Nodal Lines of Critical Random Fields\" by menglin wang (12 - Probability)
\"Optimal Stopping Problems for Real Options Driven by Short-Noise Processes\" by Ini Adinya (18 - Stochastic and Differential Modelling)
\"Stochastic Analysis of Epidemic Dynamics Under a Two-Threshold Control Policy\" by Hassane Bouzahir (18 - Stochastic and Differential Modelling)
\"Mathematical Modeling and Sensitivity Analysis of SynNotch-CAR-T Cells Identify Engineering Targets for Dynamic Tunability\" by Alexander Diefes (18 - Stochastic and Differential Modelling)
\"A Bayesian Approach in Pricing Insurance under Stochastic Gompertz Model with Health Risk Factors\" by Anjali Lomugdang (18 - Stochastic and Differential Modelling)
\"On Large Deviations in Nonlinear Filtering Theory in the Besov-Orlicz Space\" by Dina Miora (18 - Stochastic and Differential Modelling)
\"Hybridization of Stochastic Hydrological Models and Machine Learning Methods for Improving Rainfall-Runoff Modeling\" by Stephen Moore (18 - Stochastic and Differential Modelling)
\"Equity Premium in a Semimartingale Market When Jump Amplitudes Follow an Arbitrary, Normal, Binomial and Gamma Distributions While Assuming Some Selected Utility Functions\" by George Mukupa (18 - Stochastic and Differential Modelling)
\"On the Concept of Digital Pathogens and Their Impact on 'Technopandemics'\" by Farai Nyabadza (18 - Stochastic and Differential Modelling)
\"Stochastic Epidemic Models with Partial Information on Undetected Infections in the Transmission of Zika Virus\" by Lillian Oluoch (18 - Stochastic and Differential Modelling)
\"A Study of Overcompensatory Prey Growth on Discrete-Time Predator-Prey Model with Continuous and Seasonal Breeding\" by Narendra Pant (18 - Stochastic and Differential Modelling)
\"Mathematical Modelling for CTCE-9908 (a CXCR4 inhibitor) on B16 F10 Melanoma Cell Proliferation\" by Avulundiah Edwin Phiri (18 - Stochastic and Differential Modelling)
\"Can we save the Tasmanian devil and restore ecosystem balance in Tasmania? \" by Megan Powell (18 - Stochastic and Differential Modelling)
\"Boundary-Value Problems for Dynamic and Integro-Dynamic Equations on Time Scales\" by Roza Uteshova (18 - Stochastic and Differential Modelling)
\"Educational Games for Teaching Threshold Concepts in Mathematics\" by Vedrana Mikulić Crnković (19 - Mathematical Education and Popularization of Mathematics)
\"Teacher Educators’ Learning and Development in Blended Learning Contexts\" by Chanroath Monita (19 - Mathematical Education and Popularization of Mathematics)
\"Mobius equivariant maps between fields\" by Sunil Chebolu (3 - Number Theory)
\"Symmetry and the Riemann Zeta Function\" by Joseph Dillon (3 - Number Theory)
\"A Variant of the Congruent Number Problem\" by Jerome Dimabayao (3 - Number Theory)
\"Trees and valuation sequences generated by polynomials and rational functions over Z_p\" by Olena Kozhushkina (3 - Number Theory)
\"Performance of Classical Factorization Algorithms for Structured Integers\" by Isabella Li (3 - Number Theory)
\"Number Theory in Pell's Equation\" by Dr. Ruma Manandhar (3 - Number Theory)
\"A Computational Comparison of Lang-Trotter and Hardy-Littlewood Constants for CM Elliptic Curves\" by Anish Ray (3 - Number Theory)
\"Distribution of Values of Gaussian Hypergeometric Functions \" by Neelam Saikia (3 - Number Theory)
In many applications of the probabilistic method, one looks to study phenomena that occur ``with high probability''. More recently however, in an attempt to understand some of the most fundamental problems in combinatorics, researchers have been diving deeper into these probability spaces and understanding phenomena that occur at much smaller probability scales. Here I will survey a few of these ideas from the perspective of my own work in the area.
We survey explicit p-adic methods for determining sets of rational points on curves of genus 2 or more, after the work of Chabauty. This starts with the work of Coleman in 1985, which was then reframed by Kim's foundational work on Selmer varieties, and made explicit in certain cases by Balakrishnan, Besser, Dogra, Muller, Tuitman, and Vonk over the last decade. We highlight notable curves where these methods have succeeded and discuss related recent work.
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The session also welcomes work that reflects on the relationship between formal proof and other modes of mathematical reasoning, including explanation, visualization, approximation, and heuristic argument. By attending to how demonstration and persuasion have functioned within historical communities, this session aims to illuminate the dynamic interplay between mathematical rigor, communicative practice, and epistemic authority.
We summarize progress by the International Mathematical Knowledge Trust (IMKT) toward realizing the vision of a Global Digital Mathematics Library (GDML) and compare developments in the mathematical knowledge commons with those in the life sciences.The GDML strategic plan describes a system designed to “create a network of information that can be easily explored and manipulated” and argues that substantial portions of mathematical knowledge can become linked open data through a combination of machine-learning methods and editorial curation. The IMKT Charter articulates this vision of a mathematical knowledge commons grounded in open standards, persistent identifiers, and interoperable services.Fields like biodiversity informatics demonstrate how persistent identifiers (e.g. GBIF, Genbank, UniProt, iNaturalist) and community ontologies (e.g. Darwin Core, Gene Ontology) can enable fine-grained semantic annotation (e.g. Pensoft, Plazi, Biodiversity PMC) and integration (e.g. GloBI, TRY) across heterogeneous data sources. Similar ideas underpin medical information commons, astronomy's Virtual Observatory, chemistry's PubChem and, more generally, the FAIR (Findable, Accessible, Interoperable, Reusable) principles, where governance and standardized metadata enable interoperability among diverse data collections.A major milestone for mathematics is the transition of zbMATH to zbMATH Open, which now provides an openly accessible index of essentially the full peer-reviewed mathematical literature and research software, enriched with curated metadata, expert reviews, and links to external services such as arXiv, MathOverflow, OEIS, and DLMF. Although many entries link to full text, standardized deep linking to specific formulas, theorems, or conceptual entities remains under development. Additionally, it will be useful to link curated repositories such as LEAN’s mathlib, LMFDB, and MaRDI.Recent work on AI-based formula and concept discovery introduces semantic entities into mathematical metadata. This directly supports the GDML vision of combining automated semantic extraction with expert validation to make mathematical knowledge more navigable, interoperable, and machine-actionable. Together, these developments mark substantial progress toward a global mathematical knowledge commons.
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"biography": "Name: Ruma ManandharDate of Birth: 24 Aug. 1978Citizenship: NepaleseAddress: Chandragiri-6, KathmanduFamily Information: Married, and two sonsE-mail: ruma@nou.edu.np, rumamanandhar2080@gmail.comContact No: +977- 9849299654Job Position: Assistant Professor, Nepal Open UniversityKey Areas of Expertise: Abstract Algebra, Number Theory, Pedagogies, Teacher Training, Curriculum developmentAcademic Qualification: PhD in Mathematics Education from Faculty of Education, Tribhuvan University (full scholarship from World Bank via UGC Nepal)Employment Record: Teaching Mathematics in Higher Education in different Universities (More than 2 decades)Research / Study / Publications•Implication of Piaget’s Learning Theory into Instructional Strategies in Mathematics Class, Mathematics Education Forum October 2009, Vol. 2,. Year 13, Issue 26, pp 20-24, Kathmandu.•Vygotsky and Teaching Algebra, Mathematics Education Forum April 2010, Vol. I, . Year 14, Issue 27, pp 5-9, Kathmandu•APOS Theory and Teaching Concept of Cosets, Mathematics Education Forum April 2011, Vol. I, . Year 15, Issue 29, pp 32-36, Kathmandu•Reconstructing Teaching Abstract Algebra for Meaningful Learning, Mathematics Education Forum October 2012, Vol. 2,. Year 13, Issue 32, pp 8-15, Kathmandu.•Hidden Realities in learning Abstract Algebraic Ideas by Undergraduate Students, The Educator Journal August 2012, Voi. II, Year 2, Issue 2, pp 108- 117•The strategies of teaching and Learning of proof writing in abstract algebra, Mathematics Education Forum April 2014, Vol. I, Year 14, Isse 35, pp. 5- 9, Kathmandu•Sources of Learning Difficulties in Learning Abstract Algebra, Journal of Mathematics Education April 2016, Vol. I, Year 2, Issue 3, pp 16-21, Kathmandu•Strategies of Reduction of Abstraction in Abstract Algebra, International Journal of Research-Granthaalaya, November 2020, Vol. 8, Issue II, pp 245-250, Indore 452005 (M.P.) DOI: https://doi.org/10.29121/granthaalayah.v8.i11.2020.2446 •Strategies of Learning Abstract Algebra, International Journal of Research-Granthaalaya, January 2021, Vol. 9, Issue I, pp 1-6, Indore 452005 (M.P.) India DOI: https://doi.org/10.29121/granthaalayah.v9.i1.2021.2697 •Poudel, N., Manandhar, R., & Sharma, L. (2022). Students’ Transition from Grade X to CAIE A-Level: In the Context of Mathematics Curriculum in Nepal. Contemporary Mathematics and Science Education, 3(2), ep22015. https://doi.org/10.30935/conmaths/",
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"biography": "RAKOTONIRINA Dina Miora was born on February 20, 1988, in Madagascar. He is a Mathematics lecturer at the University of Antananarivo, where he has been teaching since 2015. He obtained his Advanced Studies Diploma in Mathematics in 2014, which laid the foundation for his academic and research career.His research focuses on Large Deviations in the framework of strong topology, and he has published several scientific articles in this area, contributing to the advancement of mathematical knowledge both nationally and internationally. Beyond his research, he has supervised numerous Master II students, guiding them through their theses and helping train the next generation of mathematicians and researchers.He is also actively involved in the broader mathematical community, regularly participating in conferences, seminars, and workshops, where he presents his research findings and exchanges ideas with fellow mathematicians. His work has been presented at multiple national and international conferences, reflecting his commitment to both teaching and research excellence.Through his combined efforts in teaching, research, supervision, and professional engagement, RAKOTONIRINA Dina Miora continues to make significant contributions to mathematics education and research in Madagascar and beyond.",
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"biography": "I am Dr. Vinayak S. Kulkarni working as a Professor in the Post Graduate Department of Mathematics, University of Mumbai, Maharashtra, India. I have more than 28 years teaching experience and more than 22 years research experience.I am an Applied Mathematician and did substantial research in the field of application oriented mathematics which has direct applications to real life problems in the field of Basic Sciences, Engineering and many other fields.Research Fields : My primary area is Mathematical Physics which includes Thermodynamics and Heat transfer (AMS 80A05, 80A10, 80A17, 80A19, 80A21, 80A23, 80M10, 80M20) Continuum Mechanics of Solids (AMS 74A15, 74F05, 74G75, 74H15).My secondary research area is Partial Differential Equations which includesPartial Differential Equations (AMS 35K05, 35K08, 35Q79),Integral Transforms (AMS 44A05, 44A10),Fractional Calculus (AMS 26A33, 35R11, 74S40),Applied Numerical Analysis (AMS 65N12, 65N30),Applied Analysis (AMS 97I40, 97I50, 97I99).Outline of Research: My research work is mainly dedicated to mathematical modelling followed by mathematical solutions and technical interpretation of the problems in thermodynamics and heat transfer. Thermal analysis techniques are in great demand in the basic sciences and engineering due to its ability to characterize materials and processes under various thermal conditions, ensuring product reliability and safety. It also helps understanding/ predicting thermal behavior before it's built, enabling them to identify potential problems and optimize design. Which helps to ensure materials meet specific thermal performance requirements, improving product quality and reliability. It has a wide scope of applications in diverse fields like designing of materials / structures and testing its thermal stability.My approach is mathematical analysis via well-posed mathematical modelling of the problems in the context of Boundary Value Problems involving Partial Differential Equations in the connection of classical and non-classical thermodynamics and heat transfer.I have extended my research work in the context of fractional order derivatives which is a non-local operator and it controls the memory effects of temperature changes in the system. Moreover the scientific role of order of fractional derivative is established to categorize the conducting materials in the mechanism of heat transfer.My research has multidisciplinary and transdisciplin",
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"biography": "I am a number theorist, and my research primarily focuses on studying special sequences that arise from modular forms, objects that are crucial ingredients in Wiles's proof of Fermat's last theorem as well as the formulation of the Langlands program, a theme that dictates the trends and trajectories of large parts of modern number theory. One of my research themes is to understand the prime factorization of non-zero Fourier coefficients of the quintessential Hecke eigenform, the Ramanujan Delta function. My research interests also include the study of arithmetic properties of Fourier coefficients of Hecke eigenforms, Hecke eigenvalues of Ikeda lifts, Artin’s primitive root conjecture, moments of the Riemann zeta function and L-functions associated with Hecke eigenforms, and Cilleruelo's conjecture.I was awarded the INSPIRE scholarship in 2013, and in 2016, I completed my undergraduate degree at SDM College, Ujire, India. I completed my master's degree in mathematics in 2018 from the University of Hyderabad, India. I was selected for the 'Mathematics Training and Talent Search Program' (MTTS) held at Goa University, India, in 2015, and I was selected for the 'Visiting Student Research Program' held at TIFR, Mumbai, India, in 2017. I cleared the NBHM Ph.D. scholarship exam in 2018. I obtained my Ph.D. degree titled 'Prime divisors of non-zero Fourier coefficients of Hecke eigenforms' in 2023 from the Institute of Mathematical Sciences, Chennai, India, under the guidance of Prof. Sanoli Gun. I was awarded the 'Outstanding Student Award-2024' by the Homo Bhabha National Institute (HBNI) for my Ph.D. thesis. My Ph.D. thesis comprises the following works: I improved a result of Luca and Shparlinski by proving that there exist infinitely many natural numbers n such that the values of the Ramanujan tau function at n have a large number of distinct prime factors. In joint work with Y. Bilu and S. Gun, we considered a non-archimedean analogue of a question of Atkin and Serre and derived a lower bound for the largest prime factor of values of the tau function at almost all primes, and this improves a result of Ram Murty, Kumar Murty and Saradha. In joint work with S. Gun, we derived a lower bound for the largest prime factor of values of the tau function at prime powers, improving upon a result of Bennett, Gherga, Patel and Siksek. Currently, I am a Coleman postdoctoral fellow at Queen's University, Canada, where I have the duties of both research and teaching. D",
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"biography": "† 12 - Probability\r\n\r\nVincent Vargas is a French probabilist and mathematical physicist, specialized in rigorous quantum field theory. Former student of the Ecole Normale Supérieure (2000-20004), he joined the French CNRS in 2007 as Chargé de recherche and then Directeur de recherche before joining in 2021 the university of Geneva as associate professor in a joint position between the department of theoretical physics and the department of mathematics.\r\n\r\nDuring his career, Vincent Vargas has been developing the theory of a class of random measures called Gaussian multiplicative chaos and which appear in a wide variety of fields including turbulence, quantum field theory and finance. Over the past 10 years, based on the theory of Gaussian multiplicative chaos, Vincent Vargas has developed with his collaborators Colin Guillarmou, Francois David, Antti Kupiainen and Rémi Rhodes a rigorous approach to Liouville conformal theory, which appears in the theory of two dimensional quantum gravity. \r\n\r\nWith his coauthors, he gave a rigorous probabilistic construction of the path integral formulation of Liouville theory and demonstrated it was equivalent to the celebrated bootstrap approach widely used in physics, hence bridging representation theory and probability theory.\r\nFor all these contributions, Vincent Vargas was awarded the Marc Yor prize (jointly with Rémi Rhodes) of the French academy of science in 2019, the George Polya prize (jointly with Antti Kupiainen and Rémi Rhodes) of the society for industrial and applied mathematics in 2022.\r\n\r\nPresenting jointly with Rémi Rhodes, Aix-Marseille University.",
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"biography": " Brief Academic BackgroundI, Dr. Buddhadev Pal is currently serving as an Assistant Professor in the Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, India. Since February 1, 2016, I actively engaged in teaching undergraduate (B.A./B.Sc.) and postgraduate (M.A./M.Sc.) mathematics courses.I have obtained my Ph.D. in Mathematics (Differential Geometry) from Jadavpur University, Kolkata (2010–2014), India, under the supervision of Prof. Arindam Bhattacharyya. The title of my thesis is Applications of Computational and Differential Geometry.I have completed two prestigious postdoctoral fellowships:•NBHM Postdoctoral Fellowship (Feb 2014 – Dec 2014) at Jadavpur University, under Dr. Arindam Bhattacharyya, where he continued his research in computational and differential geometry.•Dr. D.S. Kothari Postdoctoral Fellowship (Dec 2014 – Jan 2016) at the University of Calcutta, under the mentorship of Prof. Manjusha Majumdar (Tarafdar), focusing on Riemannian manifolds and their applications to the general theory of relativity.My areas of research interest include:•Riemannian and Semi-Riemannian Geometry•Differential Geometry of Curves and Surfaces•Geometric FlowsI have published more than 50 research papers as a authored or co-authored in these areas, making significant contributions to the study of differential geometry and its applications in mathematical physics.Some of them are (Last four years):YEAR 2022:[1] N. Bhunia, B. Pal and A Bhattacharyya, A new way to study on generalized Friedmann-Robertson-Walker space-time, Indian Journal of Physics, 96 (12), 3703-3711, (2022), SCIE. [2] B. Pal and S. Kumar, Characterization of proper curves and proper helix on , Hacettepe Journal of Mathematics and Statistics, 51 (5), 1288-1303, (2022), SCIE. [3] B. Pal and P. Kumar, On Riemannian Poisson warped product space, Filomat, 36 (17), 5957-5972, (2022), SCIE. [4] B. Pal and P. Kumar, Characterization of Einstein Poisson warped product space, Afrika Matematika, 33, (2022), SCOPUS.[5] B. Pal, S. Kumar and P. Kumar, Einstein warped product spaces on Lie groups, CUBO, A Mathematical Journal, 24 (03), 485-500, (2022), SCOPUS.[6] B. Pal and S. Kumar, Proper helix of order 6 and LC helix in Pseudo-Euclidean space E84, Jordan Journal of Mathematics and Statistics (JJMS),15 (4B), 2022, 1077-1092, SCOPUS.YEAR 2023:[1] B. Pal and S. Kumar, Ruled like surfaces in three dimensional Euclidean space, Annales Mathematicae et Inf",
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"biography": "I am a mathematician and academician with a strong focus on algebraic combinatorics, graph theory, and commutative algebra. Born on March 26, 1993, in Kerala, India, I have built an impressive career marked by rigorous research, teaching excellence, and numerous academic achievements. Academic Journey I earned my PhD in Mathematics from Madurai Kamaraj University (2019–2023), where my research explored the connection between combinatorics and commutative algebra under the guidance of Dr. T. Asir. Prior to this, I completed my M.Phil (2017–2019) with distinction (83.2%) and my M.Sc in Mathematics (2014–2016) from Pondicherry University. My foundational studies include a B.Sc in Mathematics (2011–2014) from Mahatma Gandhi University, Kerala.My academic prowess is further highlighted by qualifying for prestigious national exams such as the Junior Research Fellowship (JRF) and National Eligibility Test (NET) in June 2019, as well as the Tamil Nadu State Eligibility Test (TNSET) in 2018. Research Contributions I have made significant contributions to mathematical research, particularly in: Algebraic Graph Theory: Investigating Cohen-Macaulay graphs, edge ideals, and their combinatorial properties. Algebraic Combinatorics : Exploring connections with combinatorics and applications in polynomial rings. Nano Topology and Fixed Point Theory : Early work during my M.Phil on generalized feebly continuity in nano topology. I have published extensively in reputed journals such as: * Discrete Mathematics, * Communications in Algebra* Journal of Algebra and Its Applications * Bulletin of the Malaysian Mathematical Sciences Society * Expositiones Mathematicae * Discrete Applied Mathematics …My collaborative research spans national and international partnerships, including work with teachers from Sharif University of Technology (Iran) and Hanoi University of Science and Technology (Vietnam) London (UK). Teaching and Professional RolesCurrently serving as an Assistant Professor in the Department of Mathematics at Deva Matha College, Kuravilangad, Kerala, I am dedicated to innovative teaching methodologies. I have contributed as a course staff for online programs like SWAYAM (Modern Algebra, Graph Theory) and have mentored students in advanced mathematical concepts.My teaching philosophy emphasizes clarity, creativity, and the use of real-world examples to simplify abstract theories. I am proficient in programming (C, C++, Python), mathematical software (M",
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"biography": "Dr. Sarswati Shah is an applied mathematician whose research lies at the intersection of nonlinear partial differential equations (PDEs), numerical analysis, and scientific computing. Her work addresses complex multiscale problems arising in fluid dynamics, geophysics, and engineering. She specializes in hyperbolic balance laws, systems involving non-conservative products, and the design of robust numerical schemes for conservation laws. In addition to her core work, she has developed exact and delta-measure Riemann solutions and has recently extended her focus to include numerical methods for optical systems (light bending problems) and the use of neural networks to approximate solutions of PDEs.A significant part of Dr. Shah's recent work explores reduced-order modeling (ROM) techniques for high-dimensional PDEs using transport-based transforms and low-rank structures. These methods are particularly effective for improving computational efficiency in data-driven modeling and align with core concepts in machine learning such as dimensionality reduction and working in transformed feature spaces. Currently, she is designing generalizable finite element codes for a novel hyperbolic-elliptic systems using the FEniCSx framework.Her long-term research goal is to develop scalable and accurate numerical frameworks that combine classical mathematical rigor with modern computational tools to simulate nonlinear wave propagation and complex fluid behavior. She is especially interested in integrating high-resolution finite volume and finite element methods with emerging AI and machine learning techniques, particularly in settings involving shocks, dispersive waves, and nonlocal effects.Dr. Shah’s prior work includes a novel model for weakly compressible two-layer shallow water and stratified flows in complex geometries, along with the development of well-balanced finite volume schemes implemented in MATLAB and Python. Her contributions have earned her notable recognition, including the AMS-NSF Young Researcher Grant to attend the Mathematical Congress of the Americas. She also contributes actively to the academic community, co-organizing major events such as the Finite Element Circus (Fall 2025) and a minisymposium at the Joint Mathematics Meetings (JMM 2026).Since January 2025, she has been a postdoctoral researcher at George Mason University, working with Prof. Harbir Antil on interdisciplinary projects that blend applied mathematics, machine learning, and computati",
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"biography": "Franc Forstnerič graduated in Mathematics from the University of Ljubljana in 1980 and obtained PhD degree in Mathematics from the University of Washington in Seattle, USA in 1985. In the same year, he was employed by the University of Ljubljana as Assistant Professor (1986-89) and then Associate Professor (1989-93) of Mathematics. In 1991 he took the position of Visiting Professor at the University of Wisconsin-Madison in USA, where he became associate professor in 1993 and full professor in 1994. Since 2000 he is employed as a full professor by the University of Ljubljana and as researcher by IMFM, Ljubljana. \r\n\r\nForstnerič achieved his most notable results in problems of complex analysis and geometry: boundary regularity of proper holomorphic maps, polynomial convexity, proper holomorphic maps and embeddings into Euclidean spaces and other complex manifolds, holomorphic automorphisms of Euclidean spaces and their applications, construction of noncritical holomorphic functions on Stein manifolds and Stein spaces, the Oka principle and its applications, and nonlinear holomorphic approximation theory. Following a decade of research in the Oka-Grauert-Gromov theory, he introduced in the literature a new class of complex manifolds, Oka manifolds, and presented a comprehensive treatment of this subject in his monograph Stein Manifolds and Holomorphic Mappings (Springer 2011 and 2017). Oka manifolds have since become a standard notion in complex analytic geometry. In the last decade he made significant contributions to the theory of minimal surfaces and in complex contact geometry. His research has been supported over the last four decades by various funding agencies. In 2022, he received a five-year ERC Advanced Grant 2023-2027 financed by the European Comission. \r\n\r\nForstnerič received several prizes and recognitions. During PhD studies he was a Fulbright Scholar and a recipient of a Sloan Predoctoral Fellowship. In 1988 he received the Boris Kidrič prize of the Republic of Slovenia. At the University of Wisconsin, he received a Vilas Associates Award. He was elected Associate Member of the Slovenian Academy of Sciences and Arts in 1999 and Full Member in 2005. Since June 2020 he is the Academy Secretary General. In 2019, he received the Stefan Bergman Prize from the American Mathematical Society. He was a plenary speaker at the 8th European Congress of Mathematicians in 2021.",
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"biography": "Martín D. Safe is a Full Professor at the Departamento de Matemática of the Universidad Nacional del Sur (UNS), Bahía Blanca, Argentina, and an Independent Researcher at CONICET, with workplace at INMABB (Instituto de Matemática de Bahía Blanca, UNS–CONICET). Since February 2026, he serves as Dean of the Departamento de Matemática of UNS.He received his Degree in Mathematics from UNS in 2006. He obtained his Ph.D. in Computer Science from the Universidad de Buenos Aires in 2011, with a thesis on structural characterizations of graph classes related to perfect graphs and the König property, supervised by Guillermo Durán and Flavia Bonomo.His research focuses on structural and algorithmic graph theory, with emphasis on the characterization and recognition of graph classes defined by geometric intersection models (including circular-arc graphs, circle graphs, and related families) as well as their connections to perfect graph theory, combinatorial matrix theory, and combinatorial optimization. More recently, his work has expanded to include topics in analytic combinatorics and number theory (Lochs-type theorems), discrete harmonic analysis on trees (Fefferman–Stein inequalities), and network reliability.He has authored over 30 papers in peer-reviewed international journals, including SIAM Journal on Discrete Mathematics, Journal of Graph Theory, International Mathematics Research Notices (IMRN), Discrete Applied Mathematics, European Journal of Operational Research, Monatshefte für Mathematik, Graphs and Combinatorics, Linear Algebra and its Applications, and Annals of Operations Research, among others. He has also published over 15 extended abstracts in proceedings of international conferences such as LAGOS, AofA, ISCO, and SBIA.He has been an invited speaker at several major international meetings, including a plenary lecture at the IX Latin and American Algorithms, Graphs and Optimization Symposium (LAGOS 2017, Marseille, France), an invited talk at the Mathematical Congress of the Americas (MCA 2017, Montreal, Canada), an invited talk at the minisymposium on Algorithmic Graph Theory of the 8th European Congress of Mathematics (8ECM, Portorož, Slovenia, 2021), and an invited talk at the Combinatorics session of the VI Congreso Latinoamericano de Matemáticos (CLAM 2021). He has also delivered invited courses on perfect graphs and intersection graphs at various Latin American schools and meetings.He has served as co-chair of the XIII Latin and American Algor",
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"biography": "I am a 43-year-old woman, mother of two, researcher, and professor at the Federal University of Sergipe (UFS) — a university in a Brazilian state with a Human Development Index of 0.702. Throughout my academic journey, I have had the opportunity to collaborate with fellow researchers and participate in various national and international events (please visit my website: https://sites.google.com/mat.ufs.br/maria/). However, none of these compare to the ICM, as it gathers world-class mathematicians from diverse fields. Specifically, my research area, Differential Geometry, intersects with Analysis, Topology, Dynamical Systems, and Mathematical Physics. Therefore, attending the ICM will be an outstanding opportunity to engage with new problems and insights, enhancing both my professional skills and my network. My academic path began in public schools in Itabaiana, in the countryside of Sergipe, Brazil. I obtained my degree in Mathematics from UFS, a Master's degree from UFAL, and a Ph.D. from PUC-Rio. Driven by a commitment to academic advancement, I completed postdoctoral studies at IMPA and UFMG, and I am currently a Visiting Fellow at Princeton University. I began my training in Differential Geometry during my Master's, passed the rigorous qualifying exams at IMPA, and successfully transitioned into Geometric Analysis, consolidating my career with publications in high-impact journals. Resilience has been a central pillar of my journey, evidenced by my career shift after the birth of my first child and my continued engagement in cutting-edge research while working at a university in the Northeast of Brazil, distant from the country's major academic centers. I would like to highlight the following publications: - Andrade, Maria, Allan Freitas, and Diego A. Marín. \"Rigidity results for Serrin's overdetermined problems in Riemannian manifolds.\" Calculus of Variations and Partial Differential Equations, v. 64, p. 1-20, 2025. -Andrade, Maria, Tiarlos Cruz and Almir Silva Santos. \"On the σ2-curvature and volume of compact manifolds.\" Annali di Matematica Pura ed Applicata, 202.1 (2023): 367-395. -Leandro, Benedito, Maria Andrade, and Robson Lousa. \"On the geometry of electrovacuum spaces in higher dimensions.\" Annales Henri Poincaré, Vol. 24, No. 9, 2023. - Andrade, Maria, Ezequiel Barbosa, and Edno Pereira. \"Gap results for free boundary CMC surfaces in radially symmetric conformally Euclidean three-balls.\" The Journal of Geometric Analysis, 31 (2021): 8013-8035",
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"biography": "Ph.d. Theoretical Mathematics, in theory of Transcendental numbers. However, most of my recent publications are in Discrete Mathematics (Recursions, Fibonacci-Lucas numbers etc.). A sample of publications follows: Hofstadter's extraction conjecture (j. with Monteferrante) (FQ 32 (1994)), Linear recurrences in difference triangles (j with Luchins, Lemke, Tuller) (FQ 33 (1995)); Hofstadter's conjecture (Kluwer Academic Publishers Group, 1996), Recursive properties of trigonometric products (j. with Cook), Kluwer Academic Publishers, (1996)), Linear equalities in Fibonacci numbers (FQ 44 (2006)), A hierarchical parallel algorithm useful in discovering factorization identities (International Journal of Pure and Applied Mathematics 46 (2008)), Almost-recursiveness of reciprocals of linearly recurrent sequences (FQ, 49 (2011)), Sequences of the initial digits of Fibonacci numbers (j. with Barrale, Sluys) Aportaciones Mat. Investig., 20, 2011),Continued fractions consisting of alternating string patterns, (Aportaciones Mat. Investig., 20, 2011)), Extending Freitag's Fibonacci-like magic square to other dimensions (j. with Cook, Ann. Math. Inform 41(2013)), Proof of the Tojaaldi sequence conjectures (j. w Barrale, Sluys) Ann. Math inform 41 (2013)),A Cayley-Hamilton and Circulant approach to jump sums (FQ 52 (2014)), Quasi Periods for the Hofstadter Q Function (FQ 53 2015), Coefficient convergence of recursively defined polynomials (FQ 53 (2015)), Proof of the Tagiuri Histogram conjecture (FQ 57, 2019), Recursive triangles appearing embedded in recursive families (FQ 58, 2020), A method for uniformly proving a family of identities FQ 60 2022, A system of four simultaneous recursions: generalization of the Ledin-Shannon-Ollerton identity (FQ 60 2022), Sums of squares: methods for proving identity families,( Springer Proc. Math. Stat., 395), Resistance values under transformations in regular triangular grids (j. with Evans) (Discrete Applied Math 355 (2024)), Recursions and characteristic polynomials of the rows of the circuit array (j. with Evans) 62 2024). I have also published (including co-authorship in a book) on the theory of pedagogy especially as it applies to teaching mathematics. I currently teach at Towson University which has been awarded the Center of Actuarial Excellence designation and assist in teaching actuarial mathematics.",
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"biography": "Milos Stojakovic is a full professor at the Faculty of Sciences, Novi Sad. He received his PhD from the Swiss Federal Institute of Technology (ETH) in Zurich in 2005. His scientific fields of interest include Discrete Mathematics, Combinatorial Algorithms and Combinatorial Game Theory. He has authored over 40 journal papers, 20 refereed conference papers and a monograph (published by Birkhäuser, 2014). In four conferences he was an invited speaker. He is a member of the editorial board of two international academic journals. He obtained the “Dr Zoran Djindjic Award, for the best young scientist in 2008”, presented by the Provincial Secretariat for Science, Province of Vojvodina, Serbia.",
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"biography": "Ngaiming Mok left Hong Kong after high school in 1975, obtaining MA at Yale (1978) and PhD at Stanford (1980). He embarked on his career at Princeton, and was Professor at Columbia and at Paris (Orsay), before returning to Hong Kong in 1994 to be Chaired Professor at the University of Hong Kong (HKU). He became Director of the Institute of Mathematical Research at HKU since 1999, and is currently the Edmund and Peggy Tse Professor in Mathematics.\n\nMok is a leading researcher in complex geometry. He has made many research breakthroughs as testified by a dozen articles published in Annals of Mathematics, Inventiones Mathematicae, JEMS and PNAS. He distinguishes himself by the ability to cross-fertilize knowledge from different research fields to solve central problems in complex analysis, differential geometry and algebraic geometry, as evidenced by his solutions of the generalized Frankel conjecture in differential geometry, the Lazarsfeld problem and the generalized Kodaira-Spencer problem (with J.-M. Hwang) in algebraic geometry, and the Ax-Schanuel conjecture for Shimura varieties (with J. Pila and J. Tsimerman) as an analogue of a celebrated conjecture in transcendental number theory, with amazing applications to Diophantine equations. Through pioneering research Mok has built interfaces between research fields such as developing the theory of varieties of minimal rational tangents (VMRT) as a differential-geometric theory to solve many open problems in algebraic geometry. Mok has proven many definitive results on rigidity phenomena in complex geometry by exploiting also techniques from a wide range of expertise encompassing linear and nonlinear partial differential equations, Lie theory, harmonic analysis and ergodic theory. \n\nMok was Invited Speaker in ICM 1994. He is Member of the Chinese Academy of Sciences, Fellow of the Hong Kong Academy of Sciences and Fellow of the AMS.\n\nMok's academic accolades include the Sloan Fellowship (1984), the Presidential Young Investigator Award (1985), the Croucher Senior Fellowship Award (Hong Kong, 1998), the State Natural Science Award (China, 2007), the Bergman Prize (2009), the Chern Prize of the ICCM (2022), the Future Science Prize in Mathematics and Computer Science (2022), the Tan Kah Kee Award in Mathematics and Physics (CAS, 2022), and the Frontier of Science Award of the ICBS (2023). Mok served on the Fields Medal Committee for ICM 2010, and on the Selection Committee for the Shaw Prize 2023-25.",
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"biography": "I am Associate Professor of Mathematical Analysis at the Department of Mathematics \"G. Peano\", University of Turin (Italy). My main research interests and expertise concern Partial Differential Equations, Stochastic Partial Differential Equations, Fractional Partial Differential Operators, Fourier Analysis, Spectral Theory, Global Analysis on R^d and on Manifolds, Operators Algebras, Fourier Integral Operators, and Microlocal Analysis.My supervisor for the graduation thesis (in Mathematical Physics; more specifically, in General Relativity) was Prof. Fernando de Felice.My supervisors for the PhD studies were Prof. Mauro Francaviglia (first part, in Mathematical Physics and Global Analysis) and Prof. Luigi Rodino (second part, in Global Analysis and Microlocal Analysis). Prof. Rodino was the supervisor of my PhD thesis.Shortly after I got my first permanent position at the University of Turin, I have been involved in an international research and training network in Potsdam (Germany). After that, I have been a visiting scientist in Germany (Leibniz Universität Hannover), Sweden (Linnaeus Universitetet Växjö) and Serbia (University of Novi Sad), and established international research collaborations with many colleagues from those and other universities, in Italy and abroad.I have been plenary speaker, and presented contributed talks, at national and international conferences, in Italy and abroad.I have been component of the scientific council and/or of the organizing committee of national and international conferences and workshops, in Italy and abroad.I have supervised four PhD students (one in joint-supervision with the University of Hannover). I am, at present, supervisor of a fifth PhD student, in joint-supervision with the University of Paranà (Brazil). Other PhD students (from Novi Sad) have visited me, for periods of study under my supervision. One more student (from Brazil) will visit me, along the second semester of Academic Year 2025/2026, for a period of study under my supervision. I have been reviewer of PhD thesis, and component of PhD defense commissions, in Italy and in Germany.I am responsible of the local research unit at the University of Turin (Associated Investigator) of the national project (PRIN) \"Anomalies in partial differential equations and applications\" (Principal Investigator: Prof. Alessandro Palmieri, University of Bari; national project grant code 2022HCLAZ8; CUP D53C24003370006).I have been recently elected President of the In",
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"biography": "Ganga Ram Phaijoo is an assistant professor of Mathematics in the Department of Mathematics at Kathmandu University, Nepal. He completed his PhD in 2018 on modeling the dynamics of dengue disease transmission. His research interests include mathematical modeling and epidemiology, prey–predator models, numerical methods in ODEs and PDEs, computational mathematics, and blood flow dynamics, with a particular focus on the mathematical modeling of infectious disease transmission dynamics. To date, he has supervised two PhD students on dengue disease transmission dynamics with a fuzzy and fractional derivatives approach. He has been teaching undergraduate, graduate, and postgraduate students, and has supervised a number of theses/projects of undergraduate and graduate level students in the field of computational and mathematical modelling. He has participated, delivered, contributed, and given talks at several national and international conferences. He has published a number of articles in reputed national and international journals. He is involved in different mathematical activities via the Nepal Mathematical Society and the Central Department of Mathematics Alumni, Nepal. He is a technical editor of KUSET, the journal of Kathmandu University.Research Gate: https://www.researchgate.net/profile/Ganga-PhaijooGoogle Scholar: https://scholar.google.com/citations?user=CkaNSq8AAAAJhl=en",
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"biography": "My name is João Fernando Nariyoshi, and I was born in São Paulo, Brazil, in 1992. I completed my undergraduate and master’s studies at the Institute of Mathematics and Statistics of the University of São Paulo (IME-USP), where I received my B.Sc. in Applied Mathematics in 2014 and my M.Sc. in Applied Mathematics in 2017, under the supervision of Professor Orlando Lopes. In 2021, I earned my Ph.D. in Mathematics from the Institute of Pure and Applied Mathematics (IMPA), in Rio de Janeiro, under the supervision of Professor Hermano Frid. I then held a postdoctoral position at the University of Campinas (UNICAMP) from 2021 to 2023, under the supervision of Professor Marcelo Martins. Since 2023, I have served as a tenured Assistant Professor at the University of São Paulo.My research is situated in the field of partial differential equations, with particular emphasis on scalar conservation laws, kinetic formulations, stochastic degenerate parabolic-hyperbolic equations, DiPerna-Lions-Ambrosio flows, and fluid mechanics. From March 2026 to March 2027, I will be a Visiting Scholar at Pennsylvania State University, where I will collaborate with Professor Pierre-Emmanuel Jabin on problems related to averaging lemmas. I am submitting a poster based on a recent paper of mine on multidimensional conservation laws, which was accepted for publication at Archive for Rational Mechanics and Analysis.",
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"biography": "Joseph Dillon is a scientist. He grew up in Philadelphia, PA, USA, earned his BA from Ohio Wesleyan University (2003) and after a PhD from Johns Hopkins University (2010). His current research generally lies at the interface of algebraic geometry and physics, although the subject of his contribution to the ICM 2026 will focus on his investigations of Riemann’s zeta and Xi functions. This work is supported by his day job as a data scientist for a consulting firm.",
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"biography": "I have a PhD in Mathematics and work as a senior lecturer at the Department of Information Technologies of Vasyl’ Stus Donetsk National University (Vinnytsia, Ukraine). Education: Bachelor’s degree and Master’s degree in Mathematics, Vinnytsia M.Kotsiubynsky State Pedagogical University (Vinnytsia, Ukraine); PhD study at Khmelnitskiy National University (Khmelnitskiy, Ukraine); PhD obtained at Vasyl Stefanyk Precarpathian National University (Ivano-Frankivsk, Ukraine) in 2019. The title of the PhD thesis is “Orthogonality of multiary operations and algorithms of their construction’’, it was completed under the supervision of Fedir Sokhatsky, Dr. Sc., associate professor.My academic interests are in combinatorics, algebra, and discrete mathematics with a focus on discrete algebraic structures such as n-ary operations and the corresponding hypercubes, quasigroups and Latin hypercubes with the orthogonality property. The main contributions of my PhD thesis are an invertibility criterion for a composition of two multiary operations; an algorithm for constructing orthogonal multiary operations; an algorithm for complementing a k-tuple of orthogonal n-ary operations (and a k-tuple of orthogonal k-ary operations) to an n-tuple of orthogonal n-ary operations and some estimations of the numbers of these complements etc.Currently, the major emphasis of my research is on the study of parastrophic-orthogonal ternary quasigroups, their existence, and related problems.A series of research papers has been published in peer-reviewed journals (https://orcid.org/0000-0002-5609-0434), particularly in journals indexed in Scopus and Web of Science. I regularly participate in scientific events and have received funding to attend and present my research results at major international conferences and congresses including 9ECM, ICIAM 2023 Tokyo, ICIAM 2019, ICM 2018, and others. The complete list of conferences, congresses and workshops consists of over 25 events; among them, the most important conferences in recent years include:- the International conference “Quasigroups and Related Systems” (ConfQRS-2025), July 2-4, 2025, Moldova State University, Chisinau, Republic of Moldova; - 15 Ukraine Algebra Conference, 8-12 July, 2025, Ivan Franko National University of Lviv, Lviv, Ukraine; - 9th European Congress of Mathematicians (9ECM), July 15th to 19th, 2024, University of Seville, Sevilla, Spain; - Conference LOOPS’23 and Workshop LOOPS’23, June 25 - July 2, 2023, Bedlewo, Poland;",
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"biography": "Xiao-Shan Gao is a professor in the Academy of Mathematics and Systems Science, Chinese Academy of Sciences. He works in the fields of computational algebraic geometry, symbolic computation, and mathematical theory of deep learning. He had published over 160 research papers. http://www.mmrc.iss.ac.cn/~xgao",
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"biography": "Yurii Nesterov was graduated from Moscow State University in 1977. He received Ph.D. degree in Applied Mathematics in 1984 at Institute of Control Sciences in Moscow. From 1977 to 1992, he worked as a researcher at Central Economical and Mathematical Institute of Russian Academy of Sciences. At that time, his research interests were concentrated on development of Fast Gradient Methods, theory of Lexicographic Differentiation for non-differentiable functions, and development of Polynomial-Time Interior-Point Methods based on the general theory of self-concordant functions.\r\n\r\nIn the period 1993 – 2024, he worked as professor at Center of Operations Research and Econometrics in Catholic University of Louvain (Belgium). The topics of his research were quite diverse: polynomial-time methods for Linear Matrix Inequalities, convex relaxations of NP-hard problems, Smoothing Techniques, global performance analysis of second-order methods, specific methods for huge-scale optimization problems, implementable tensor methods, bi-level optimization and universal mixed-order optimization schemes.\r\n\r\nAfter retirement in September 2024, Yurii Nesterov keeps a position of Emeritus Professor at UCLouvain. In 2024-2026, he was a Research Professor at Corvinus University of Budapest. Starting from 2026, he has a joint position at CUHK(Shenzhen) and Shenzhen Loop Area Institute (China). His main research topic now is the development of accelerated methods for new problems arising in Machine Learning and Artificial Intelligence.\r\n\r\nYurii Nesterov is an author of 6 monographs and more than 150 refereed papers in the leading optimization journals. He got several high-level international recognitions, including the following lifetime achievement awards:\r\n•\tDantzig Prize from SIAM and Mathematical Programming society (2000), \r\n•\tJohn von Neumann Theory Prize from INFORMS (2009), \r\n•\tEuro Gold Medal from Association of European Operations Research Societies (2016). \r\n•\tWorld Laureates Association Prize (2023).\r\n•\tAcademy Award of National Academy of Artificial Intelligence (2026)\r\n\r\nHe is an International Member of National Academy of Sciences (USA), member of Academia Europaeae, and Montenegrin Academy of Sciences.",
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"biography": "\"My research area is at the meeting point of symplectic/contact topology and complex algebraic geometry/singularity theory. I have worked on problems concerning the classification of symplectic fillings of links of surface singularities and considered the implications of these to the smoothings of complex surface singularities. In particular, I have, with K. Ono, classified the symplectic filling of links of quotient surface singularities (see [1]); with B. Ozbagci, studied the topology of symplectic fillings of links of cyclic quotient singularities, leading to the discovery that all such fillings, and hence all smoothing of cyclic quotient singularities, are related via rational blowdowns/blowups (see [2],[3]); and with A. Stipsicz, completed the classification of all weighted homogeneous surface singularities which have rational homology disk smoothing, a problem which had interested mathematicians since the 1980's (see [4]). In earlier research, I have worked on generating functions in contact/symplectic geometry and, in particular, used these to construct a partial order on the space of contactomorphisms of R^{2n+1} (see [5]). Presently, with S. Finashin, I have been working on describing all sections of rational elliptic Lefschetz fibrations via their monodromy representations (see [6]).",
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"biography": "Jean-Marc Schlenker is a professor at the University of Luxembourg since 2013. He obtained his PhD in 1994, under the direction of François Labourie, and was then assistant professor at Université Paris-Saclay (Orsay) from 1995 to 2000, and professor at the Université Paul Sabatier (Toulouse III) from 2000 to 2013.\r\n\r\nHis core research lies in differential and low‑dimensional geometry and topology, particularly hyperbolic or anti-de Sitter geometry, Teichmüller theory, and polyhedral geometry, sometimes with motivations from mathematical physics. His research includes works on the geometry of 3-dimensional hyperbolic manifolds with convex boundaries, on the renormalized volume of hyperbolic 3-manifolds, or on maximal surfaces in anti-de Sitter geometry. He has benefitted from working with a number of regular collaborators, such as Francesco Bonsante, Kirill Krasnov, Qiyu Chen, Jeffrey Danciger, Thierry Barbot, and Sara Maloni. He also has worked in other fields of mathematics, or in interdisciplinary collaborations with other fields. \r\n\r\nSchlenker has held significant administrative and scientific responsibilities in France, as well as in Luxembourg, where he was dean of his faculty from 2018 to 2023.",
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"biography": "Current Academic CareerCertified Professor of Mathematics and Doctor of Pure Mathematics.Personal InformationFull Name: RAKOTO Jean JollyDate of Birth: Around 1959, Sahafia (Vangaindrano)Marital Status: MarriedProfession: EducatorNationality: MalagasyNational Service: Outside of the People’s Armed Forces, at Lycée Morondava (1979-1980).Areas of ExpertiseDifferential Geometry, Discrete Geometry, Educational Sciences, Rural DevelopmentQualities and AbilitiesOrganized, responsible, precise, good interpersonal skills. Understanding, dynamic, rigorous,serious, integral, organized, and decisive.Research InterestsDiscrete Geometry, Convex Polytopes and Polyhedra, Coding and Decoding Theories, ImageProcessing, Educational SciencesAcademic Career• Since 2023: Head of Discrete Geometry Course at the École Normale Supérieure,University of Toamasina, Madagascar.• Since 2017: Associate Professor at the University of Antananarivo, Madagascar.• 2014 - 2016: Adjunct Lecturer at the École Supérieure Polytechnique of Antsiranana,University of Antsiranana, Madagascar.• 2004 - 2016: Mathematics Teacher at Lycée Mixte Ambohijery, Ambilobe.• 1987 - 2006: Teacher at CEG PK3 Antsiranana I.• 1984 - 1987: Teacher at CEG Anaborano Ifasy (Ambilobe), Madagascar.• 1982 - 1984: Teacher at E.P.P Anaborano Ifasy (Ambilobe), Antsiranana, Madagascar.EducationDegrees and Certificates:• 2016: PhD in Mathematics, University of Antananarivo• 2013: Diplôme d’Études Approfondies (DEA) in Mathematics and Computer Science,University of Antananarivo• 2004: Attestation of Advanced Studies (AEA) in Mathematics and Computer Science,University of Antananarivo• 2003: Teaching Certificate in Mathematics (CAPEN), École Normale Supérieure,University of Fianarantsoa• 2000: Pedagogical Aptitude Certificate for First Cycle Teaching (CAPESPC), SectionMaths-Phys, INFP Mahamasina, Antananarivo• 1979: Baccalaureate, Series C, Lycée Laurent Botokeky, ToliaraInternships• 2003: Mathematics Teacher at Lycée Moderne d'Ampefiloha• 2000: Mathematics-Physics Teacher at CEG TsimbazazaThesis and Research• 2013: Thesis preparation on \"On the Family of Ehrhart Polynomials andCounterexamples to Beck's Conjecture\" (Ongoing PhD).• 2013: Thesis on \"Ehrhart Polynomial Theory\" (DEA).• 2003: Thesis on \"The Octonions\" (CAPEN).• 2000: Thesis on \"The Impact of Fishermen’s Departures on School Dropout Rates atCEG PK3 Antsiranana I\" (CAPESPC).Publications• Second author of \"Application of a Special Polynomial to an EntropicogeneticCoding",
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"biography": "George A. Anastassiou short BiographyGeorge A. Anastassiou was born in Athens, Greece in 1952.He received his B.SC degree in Mathematics from Athens University, Greece in 1975.He received his Diploma in Operations Research from Southampton University, UK in 1976.He also received his MA in Mathematics from University of Rochester, USA in 1981.He was awarded his Ph. D in Mathematics from University of Rochester, USA in 1984.During 1984-86 he served as a visiting assistant professor at the University of Rhode Island, USA.Since 1986 till 2024, he had been a faculty member at the University of Memphis, USA.He had been a full Professor of Mathematics since 1994.Since August 2024 is a Professor Emeritus.His research area is “Computational Analysis” in the very broad sense.He has published over 750 research articles in international mathematical journals and over 58-monographs, proceedings and textbooks in well-known publishing houses.Several awards have been awarded to George Anastassiou.In 2007 he received the Honorary Doctoral Degree from University of Oradea, Romania.He is associate editor in over 93 international mathematical journals and had been editor in-chief in 3 journals, most notably in the well-known “Journal of Computational Analysis and Applications”.G. ANASTASSIOU ON THE TOP 2% IN RESEARCHGATE.NET:https://www.researchgate.net/profile/George-Anastassiou/statsG. ANASTASSIOU ON THE WORLD’S TOP2%:https://www.memphis.edu/mediaroom/releases/2023/december/uofm-research-top-2-percent-stanford-elsevier.phphttps://topresearcherslist.com/Home/Profile/1149671Well done, George!With 162 new reads, your research items were the most read research items from your department last weekAchieved on November 17, 2024https://www.researchgate.net/profile/George-Anastassiou/achievement/673b162069976e3d9f419979THIS HAPPENING EVERY WEEK FOR THE LAST MANY MANY YEARS!https://www.researchgate.net/profile/George-Anastassiou/achievement/68f5f092fa300b1155b5eefd",
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"biography": "EDUCATION:(1999-2002) Doctora de la Universidad de Buenos Aires, Área Ciencias Matemática [Ph. D., Mathematics], Argentina.(1994-1998) Licenciada en Ciencias Matemáticas, FCEN, Universidad de Buenos Aires, Argentina (UBA)CURRENT POSITIONS: 08/2024-Head of the Department of Mathematics, FCEN, Universidad de Buenos Aires, Argentina (UBA).05/2023- Full Professor, Department of Exact Sciences, CBC-UBA.07/2022-Principal Researcher, National Council of Scientific Research, Argentina (CONICET).11/2019- Associate Professor, Department of Mathematics, FCEN-UBA.PREVIOUS POSIITONS:2012-2023 Associate Professor, Department of Exact Sciences, CBC-UBA.2012-2022 Independent Researcher, CONICET.2010-2011 Assistant Professor, Department of Exact Sciences, CBC-UBA.2008-2012 Adjunct Researcher, CONICET.2006-2019 Assistanta Professor, Department of Mathematics, FCEN-UBA.2005-2007 Assistant Researcher, CONICET.1999-2005 Graduate teaching assistant, Department of Mathematics, FCEN-UBARESEARCH INTERESTS:My fields of expertise are Computational Commutative Algebra and Algebraic Geometry, with an emphasis in efficiency and complexity of algorithms to solve problems related to polynomials. My research includes elimination theory, algorithmic solving of multivariate polynomial equation systems, certificates of positivity for real polynomials, and applications. In addition, I am interested in effective Differential Algebra, mainly in the study of algorithmic aspects related to solving differential algebraic equation systems.RECENT PUBLICATIONS:- Herrero, María Isabel; Jeronimo, Gabriela; Sabia, Juan. Sparse systems and algorithmic equidimensional decomposition (2025). To appear in Appl. Algebra Engrg. Comm. Comput.- D’Andrea, Carlos; Jeronimo, Gabriela. Sparse Nullstellensatz, resultants and determinant of complexes. International Mathematics Research Notices (IMRN), Volume 2025, Issue 12, rnaf 174.- Jeronimo, Gabriela; Lanciano, Leonardo; Solernó, Pablo. On the geometric degree of the tangent bundle of a smooth algebraic variety. Collect. Math. (2025). https://doi.org/10.1007/s13348-025-00474-y- Español, Malena; Jeronimo, Gabriela. Local convergence analysis of a variable projection method for regularized separable nonlinear inverse problems. SIAM J. Matrix Anal. Appl. 46, No. 2 (2025), pp. 858-878.- Jeronimo, Gabriela; Perrucci, Daniel. Rational certificates of non-negativity on semialgebraic subsets of cylinders. J. Pure Appl. Algebra, Vol. 228, Issue 6 (2024), 107596.- Barbagallo",
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