## Programs & Events

##### Neural Coding and Combinatorics

Oct 30 - Nov 3, 2023

Cracking the neural code is one of the longstanding questions in neuroscience. How does the activity of populations of neurons represent stimuli and perform neural computations? Decades of theoretical and experimental work have provided valuable clues about the principles of neural coding, as well as descriptive understandings of various neural codes. This raises a number of mathematical questions touching on algebra, combinatorics, probability, and geometry. This workshop will explore questions that arise from sensory perception and processing in olfactory, auditory, and visual coding, as well as properties of place field codes and grid cell codes, mechanisms for decoding population activity, and the role of noise and correlations. These questions may be tackled with techniques from information theory, mathematical coding theory, combinatorial commutative algebra, hyperplane arrangements, oriented matroids, convex geometry, statistical mechanics, and more.

##### 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