## Programs & Events

##### Harmonic Analysis and Convexity

Sep 7 - Dec 9, 2022

In recent years, the interaction between harmonic analysis and convex geometry has dramatically increased, which resulted in solutions to several long-standing problems. The program will bring together leading mathematicians in both areas, along with researchers working in related applied fields, for the first-ever long-term joint program.

The main directions of the program will include: the Fourier approach to Geometric Tomography, the study of geometric properties of solids based on information about their sections and projections, Volume and Duality, Bellman technique for extremal problems of harmonic analysis, and various types of convexity of solutions of corresponding Hamilton–Jacobi–Bellman equation, as well as numerical computations and computer-assisted proofs applied to the aforementioned problems. The computational part will cover theoretical aspects (optimal algorithms, and why they work) as well as more applied ones (implementation).

##### Organizing Committee

- Javier Gomez Serrano
- Irina Holmes Fay
- Bo'az Klartag
- Alexander Koldobskiy
- Sergei Treil
- Alexander Volberg
- Artem Zvavitch

##### Discrete Optimization: Mathematics, Algorithms, and Computation

Jan 30 - May 5, 2023

Discrete optimization is a vibrant area of computational mathematics devoted to efficiently finding optimal solutions among a finite or countable set of possible feasible solutions.

A famous and classical example of a problem in discrete optimization is the *traveling salesperson problem*: For given cities and distances of traveling from one city to another, we seek to find the shortest route that visits each city once and returns to the starting city. Discrete optimization problems naturally arise in many kinds of applications including bioinformatics, telecommunications network design, airline scheduling, circuit design, and efficient resource allocation. The field also connects to a variety of areas in mathematics, computer science, and data analytics including approximation algorithms, convex and tropical geometry, number theory, real algebraic geometry, parameterized complexity theory, quantum computing, machine learning, and mathematical logic.

The semester program... (more)

##### Organizing Committee

- Jesús De Loera
- Antoine Deza
- Marcia Fampa
- Volker Kaibel
- Jon Lee
- Laura Sanità

##### Math + Neuroscience: Strengthening the Interplay Between Theory and Mathematics

Sep 6 - Dec 8, 2023

The goal of this semester program is to bring together a variety of mathematicians with researchers working in theoretical and computational neuroscience as well as some theory-friendly experimentalists. However, unlike programs in neuroscience that emphasize connections between theory and experiment, this program will focus on building bridges between theory and mathematics. This is motivated in part by the observation that theoretical developments in neuroscience are often limited not only by lack of data but also by the need to better develop the relevant mathematics. For example, theorists often rely on linear or near-linear modeling frameworks for neural networks simply because the mathematics of nonlinear network dynamics is still poorly understood. Conversely, just as in the history of physics, neuroscience problems give rise to new questions in mathematics. In recent years, these questions have touched on a rich variety of fields including geometry, topology, combinatorics,... (more)

##### Organizing Committee

- Carina Curto
- Brent Doiron
- Robert Ghrist
- Kathryn Hess
- Zachary Kilpatrick
- Matilde Marcolli
- Konstantin Mischaikow
- Katie Morrison
- Elad Schneidman
- Tatyana Sharpee

##### Numerical PDEs: Analysis, Algorithms, and Data Challenges

Jan 29 - May 4, 2024

This semester program will bring together both leading experts and junior researchers to discuss the current state-of-the-art and emerging trends in computational PDEs. While there are scores of numerical methodologies designed for a wide variety of PDEs, the program will be designed around three workshops each centered around a specific theme: PDEs and Geometry, Nonlocal PDEs, and Numerical Analysis of Multiphysics problems. This grouping of topics embodies a broad representation of computational mathematics with each set possessing their own skill set of mathematical tools and viewpoints. Nonetheless, all workshops will have the common theme of using rigorous mathematical theory to develop and analyze the convergence and efficiency of numerical methods. The diversity of the workshop topics will bring together historically distinct groups of mathematicians to interact and facilitate new ideas and breakthroughs.

##### Organizing Committee

- Marta D'Elia
- Johnny Guzman
- Brittany Hamfeldt
- Michael Neilan
- Maxim Olshanskii
- Sara Pollock
- Abner Salgado
- Valeria Simoncini

##### Theory, Methods, and Applications of Quantitative Phylogenomics

Sep 4 - Dec 6, 2024

A fundamental challenge that spans nearly all areas of evolutionary biology is the development of effective techniques for analyzing the unprecedented amount of genomic data that has become readily available within the last decade. Such data present specific challenges for the area of phylogenetic inference, which is concerned with estimating the evolutionary relationships among collections of species, populations, or sequences. These challenges include development of evolutionary models that are sufficiently complex to be biologically realistic while remaining computationally tractable; deriving and implementing algorithms to efficiently estimate phylogenetic relationships that use models whose theoretical properties are well-understood and therefore interpretable; and devising ways to scale novel methodology developed to handle datasets that are increasingly large and complex.

This semester program brings together mathematicians, statisticians, computer scientists, and experimental... (more)

##### Organizing Committee

- Elizabeth Allman
- Cécile Ané
- Elizabeth Gross
- Laura Kubatko
- Simone Linz
- Siavash Mirarab
- John Rhodes
- Sebastien Roch
- Leo van Iersel

##### Geometry of Materials, Packings and Rigid Frameworks

Jan 29 - May 2, 2025

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 is 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... (more)

##### Organizing Committee

- Alexander Bobenko
- Philip Bowers
- John Bowers
- Robert Connelly
- Steven Gortler
- Miranda Holmes-Cerfon
- Sabetta Matsumoto
- Anthony Nixon
- Meera Sitharam