Conferences  >  Mathematics  >  Geometry and Topology  >  United States

Institute for Computational and Experimental Research in Mathematics (ICERM)

In recent years, there has been a significant increase in the interaction between harmonic analysis and convex geometry, leading to solutions for several longstanding open problems, the discovery of new phenomena, as well as many new intriguing open questions. These connections were studied during the Fall 2022 ICERM semester program Harmonic Analysis and Convexity. The objective of this workshop is to revisit and review the results produced during the semester and the subsequent year. The primary areas of focus for the workshop will encompass: The Fourier approach to Geometric Tomography; Volume and Duality; the Bellman technique for extremal problems in harmonic analysis; Convexity of solutions to Hamilton–Jacobi–Bellman equations; as well as numerical computations and computer-assisted proofs: Exploring the use of computational methods for theoretical aspects, including optimal algorithms, as well as practical implementation.

ICERM;     Email: info@icerm.brown.edu

harmonic analysis, convex geometry, computation and computer-assisted proofs

Institute for Computational and Experimental Research in Mathematics (ICERM)

Given an incidence structure, one may model a variety of geometric problems. This Semester Program will revolve around two fundamental examples and their applications to modern challenges in the study, analysis, and design of materials. (1) Packings and patterns of circles where the underlying combinatorics are mixed with advanced geometric concepts and strong links are made to discrete differential geometry. (2) The rigidity and flexibility of bar-joint structures where real algebraic geometry is intertwined with sparse graph theory and matroidal techniques. A prime objective of the program is to advance the applicability of these topics to fundamental applications, most notably in statistical physics and materials science.

The program will integrate diverse fields of discrete mathematics, geometry, theoretical computer science, mathematical biology, and statistical and soft matter physics. Various workshops will be designed to attract both theoretical and applied practitioners and to stimulate the cross-fertilization of ideas between these disparate communities.

ICERM;     Email: info@icerm.brown.edu

Metallurgy and Materials Science,    Thermodynamics, Fluid Dynamics and Statistical Physics

The SCGAS is an annual conference on geometric analysis and related fields hosted jointly by UC Irvine and UC San Diego.

The 2025 SCGAS conference will feature the following speakers:

Simon Brendle (Columbia University)

Alice Chang (Princeton University)

Pengfei Guan (McGill University)

Lan-Hsuan Huang (University of Connecticut)

Christos Mantoulidis (Rice University)

Valentino Tosatti (New York University)

Ryan Unger (Stanford University)

Differential Geometry, Geometric Analysis

Analysis,    Calculus, Differential Equations and Integration

Institute for Computational and Experimental Research in Mathematics (ICERM)

This workshop brings together researchers from three distinct streams of mathematics: the classical rigidity theory of bar-joint and tensegrity frameworks in combinatorics and discrete geometry; the theory of generalized circle packing that arose from the study of 3-manifolds in geometric topology, extending to sphere packing and jamming; and discrete differential geometry. A scattering of results in recent years has started to forge connections among these fields. The main aim of the workshop is to encourage their cross-fertilization, with particular emphasis on the rigidity of inversive distance packings. Participants will attend presentations on cutting-edge research and initiate new collaborations.

ICERM;     Email: info@icerm.brown.edu

Applied Mathematics (in general),    Metallurgy and Materials Science

Institute for Computational and Experimental Research in Mathematics (ICERM)

This workshop will be centered on recent advances in graph rigidity and interactions between rigidity, algebraic statistics, and matroid theory. Three major advances are the recent resolution of the matroid maximality conjecture, the newly developed link to maximum likelihood estimation in Gaussian graphical models, and the recent positive resolution of Lovasz and Yemini's connectivity conjecture for generic rigidity. The workshop will showcase a diverse sample of current work addressing fundamental problems in graph rigidity, algebraic matroids, and algebraic statistics.

ICERM;     Email: info@icerm.brown.edu

Institute for Computational and Experimental Research in Mathematics (ICERM)

The geometric arrangement of a material’s constituents plays an important role in governing its behavior. Concepts from discrete mathematics to describe these geometric arrangements, including notions of rigidity and flexibility, can bring fundamental insight into how a material might respond to stress, be designed, be reconfigured, etc. Beyond materials, the notions of network rigidity can be applied to more abstract networks and geometries, such as those found in data science. This workshop aims to build connections between the field of mathematical rigidity theory, other topics in applied mathematics, and related areas of science and engineering.

ICERM;     Email: info@icerm.brown.edu

Graph Theory and Combinatorics,    Chemicals and Materials Science