
Probability and Statistics of Discrete Structures
Organizers: Louigi AddarioBerry (McGill University), Christina Goldschmidt (University of Oxford), PoLing Loh (University of Cambridge), Gabor Lugosi (ICREA), Dana Randall (Georgia Institute of Technology), LEAD Remco van der Hofstad (Technische Universiteit Eindhoven)This program is devoted to the study of the probabilistic and statistical properties of such networks. Central tools include graphon theory for dense graphs, local weak convergence for sparse graphs, and scaling limits for the critical behavior of graphs or stochastic processes on them. The program is aimed at pure and applied mathematicians interested in network problems.
Updated on Feb 29, 2024 02:57 PM PST 
Extremal Combinatorics
Organizers: LEAD David Conlon (California Institute of Technology), LEAD Jacob Fox (Stanford University), Penny Haxell (University of Waterloo), Janos Pach (New York University, Courant Institute), Maya Stein (Universidad de Chile), Andrew Suk (University of California, San Diego)Extremal combinatorics concerns itself with problems about how large or small a finite collection of objects can be while satisfying certain conditions. Questions of this type arise naturally across mathematics, so this area has close connections and interactions with a broad array of other fields, including number theory, group theory, model theory, probability, statistical physics, optimization, and theoretical computer science.
Updated on Feb 29, 2024 02:56 PM PST 
Kinetic Theory: Novel Statistical, Stochastic and Analytical Methods
Organizers: Laurent Desvillettes (Université Paris Cité), Irene M. Gamba (University of Texas, Austin), Francois Golse (Centre de Mathématiques Laurent Schwartz, École Polytechnique), LEAD Pierre Emmanuel Jabin (Pennsylvania State University), Qin Li (University of WisconsinMadison), Chiara Saffirio (Universität Basel), Weiran Sun (Simon Fraser University), Lexing Ying (Stanford University)The focus of the proposed program is on socalled kinetic equations, describing the evolution of the of manyparticle interacting systems. These models have the form of statistical flows, with their solutions being either a single or multiple point probability density functions or measures, supported in a space of attributes. The attributes are problemdependent and can be molecular velocity, energy, opinion, wealth, and many others. The flow then predicts the evolution of the probability measure in time, position in space, and the interchanging of the particles' states by the transition probability.
The program will strive to give an overview of the novel mathematical tools used in kinetic theory through a broad range of classical and more recent applications.
Updated on Aug 29, 2024 07:56 PM PDT 
Recent Trends in Stochastic Partial Differential Equations
Organizers: Sandra Cerrai (University of Maryland), Yu Gu (University of Maryland), Massimiliano Gubinelli (University of Oxford), Davar Khoshnevisan (University of Utah), Andrea Nahmod (University of Massachusetts, Amherst), Hao Shen (University of WisconsinMadison), LEAD Lorenzo Zambotti (Sorbonne Université)The topic Singular Stochastic Partial Differential Equations (singular SPDE) has rapidly grown to be an active research area at the interface of Stochastic Analysis and PDEs on one hand, and Mathematical Physics on the other hand. During this decade we have witnessed a series of tremendous breakthroughs in the solution theories of SPDEs, universality problems, largescale asymptotic behaviors of solutions, and foundational relations with quantum field theories and geometry. Many longstanding problems have been resolved via newly developed methods – notably the theories of regularity structures and paracontrolled distributions – and deep connections with other fields are quickly emerging.
It is a natural time to convene a largescale semester program.
Updated on Jul 09, 2024 04:18 PM PDT 
Geometry and Dynamics for Discrete Subgroups of Higher Rank Lie Groups
Organizers: Martin Bridgeman (Boston College), LEAD Richard Canary (University of Michigan), Amir Mohammadi (University of California, San Diego), LEAD Hee Oh (Yale University), Maria Beatrice Pozzetti (RuprechtKarlsUniversität Heidelberg), JeanFrançois Quint (CNRS  Université de Montpellier)This research program will bring together two intellectual communities that have made significant advances in the study of discrete subgroups of higher rank semisimple Lie groups: the homogeneous dynamics community and the community studying geometric structures and Anosov groups.
Updated on Apr 17, 2024 11:08 AM PDT 
Topological and Geometric Structures in Low Dimensions
Organizers: Ian Agol (University of California, Berkeley), Kenneth Bromberg (University of Utah), Sebastian Hensel (LMU München), Christopher Leininger (Rice University), Kathryn Mann (Cornell University), LEAD Yair Minsky (Yale University), Rachel Roberts (Washington University in St. Louis)Low dimensional topology is a meeting place for many objects and ideas from diverse areas of mathematics, including foliation theory, geometry, and smooth and conformal dynamics. For instance, many foliations on 3manifolds admit transverse flows, connecting (local) leafwise homeomorphisms to flow dynamics and the mapping class groups of the leaves. Leafwise conformal or hyperbolic structures can be approached through Teichmüller theory, and connect again to onedimensional dynamics through "universal circles" organizing compactifications of all the leaves or of the flow space. Many of these ideas originate in work of Thurston but in recent years have diverged and are ripe for reconnection.
The program will bring together experts in all these fields together with younger researchers, who together can form new connections and open new areas for exploration.Updated on Jul 09, 2024 04:16 PM PDT 
Representation Theory Under the Influence of Quantum Field Theory
Organizers: David BenZvi (University of Texas, Austin), LEAD Tudor Dimofte (University of Edinburgh), Iva Halacheva (Northeastern University), Joel Kamnitzer (University of Toronto), Pavel Safronov (University of Edinburgh), Peng Shan (Tsinghua University)The upcoming SLMath program is organized around key themes of “higher” quantization and mirror symmetry as they impact and elucidate a wide variety of questions in representation theory. The program will bring together experts and young researchers from algebra, geometry, physics and number theory to help develop and disseminate this unified vision of a rapidly evolving field, exploring the mathematical consequences of the examples, structures, and dualities discovered in physics.
Updated on Jul 23, 2024 02:57 PM PDT 
Motivic Homotopy Theory: connections and applications
Organizers: Aravind Asok (University of Southern California), Adrien Dubouloz (Institut de Mathématiques de Bourgogne), Elden Elmanto (University of Toronto, Scarborough; Harvard University), Daniel Isaksen (Wayne State University), PaulArne Ostvaer (Università di Milano), Anand Sawant (Tata Institute of Fundamental Research), Kirsten Wickelgren (Duke University), Maria Yakerson (University of Oxford)Tremendous progress has been made using motivic techniques in geometric questions for affine algebraic varieties, especially those involving algebraic vector bundles. Computations in classical algebraic topology have been improved by motivic techniques, e.g., related to the problem of computing homotopy groups of spheres. Moreover, the theory has identified new structures of interest in arithmetic situations. Transformative recent progress in motivic homotopy theory has only broadened the scope for potential applications of motivic techniques, as well as new avenues of interaction with other areas of mathematics. This program will build on previous successes, explaining the tools that have been developed and how to use them, analyzing questions of the sort described above and identifying new domains where motivic techniques will be successful.
Updated on Jul 23, 2024 02:37 PM PDT 
New Trends in Tropical Geometry
Organizers: Pierrick Bousseau (University of Georgia), Melody Chan (Brown University), Ilia Itenberg (Institut de Mathématiques de Jussieu  Paris Rive Gauche), Hannah Markwig (EberhardKarlsUniversität Tübingen), LEAD Kris Shaw (University of Oslo)Tropical geometry can be viewed as a degenerate version of algebraic geometry,where the role of algebraic varieties is played by certain polyhedral complexes. As the degeneration process, called tropicalization, preserves many fundamental properties, tropical geometry provides important bridges and an exchange of methods between algebraic geometry, symplectic geometry and convex geometry; these links have been extremely fruitful and gave rise to remarkable results during the last 20 years. The main focus of the program will be on the most significant recent developments in tropical geometry and its applications. The following topics are particularly influential in the area and will be central in the program:
 real aspects of tropical geometry;
 tropical mirror symmetry and nonArchimedean geometry;
 tropical phenomena in symplectic geometry;
 matroids, combinatorial and algebraic aspects;
 tropical moduli spaces;
 tropical geometry and A1homotopy theory.
Updated on Mar 13, 2024 02:34 PM PDT 
Inverse Problems and Applications
Organizers: Fioralba Cakoni (Rutgers University), Maarten de Hoop (Rice University), Anna Gilbert (Yale University), Katya Krupchyk (University of California, Irvine), Matti Lassas (University of Helsinki), LEAD Gunther Uhlmann (University of Washington)Inverse problems (IP) arise in all fields of science and technology where a cause for an observed or desired effect is sought. In the last 50 years or so there has been substantial progress in the mathematical understanding of these problems but many questions remain open. The mathematics of these problems involves many areas in Mathematics including PDE, differential geometry, integral geometry, probability, statistics, complex analysis, numerical analysis, mathematical physics, data science, etc. Since the 2010 program at the thenMathematical Sciences Research Institute (now Simons Laufer Mathematical Sciences Institute), there has been significant progress in inverse problems; many of the advances can be traced back to that program. However, there are still deep open questions remaining as well, some of which are discussed in this proposal. New research topics include the connection between IP and machine learning, IP for nonlinear equations, IP for nonlocal operators, and connections between statistics and IP.
Updated on Feb 28, 2024 03:01 PM PST

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