Programs & Events
Numerical PDEs: Analysis, Algorithms, and Data Challenges
Jan 29 - May 3, 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 its 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 Olshanskiy
- 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
- Barbara Holland
- 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 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... (more)
Organizing Committee
- Alexander Bobenko
- Philip Bowers
- John Bowers
- Robert Connelly
- Steven Gortler
- Miranda Holmes-Cerfon
- Sabetta Matsumoto
- Anthony Nixon
- Meera Sitharam
Categorification and Computation in Algebraic Combinatorics
Sep 3 - Dec 5, 2025
âAlgebraic combinatoricsâ can be thought of as âcounting thingsâ and ârepresentation theoryâ can be thought of as the âstudy of symmetryâ. The notions of âcountingâ and âsymmetryâ are all-pervasive in the natural sciences â thus the pure mathematical questions we consider often have ramifications across physics, quantum theory, chemistry, cryptography. . .
The past decade has been one of the most exciting and fruitful times in the history of combinatorics and representation theory. One of the overarching themes in this story is the search for richer structures which secretly underpin the classical problems in the field â these might manifest themselves as algebraic or geometric structures, or even as diagrammatic categories.
The discovery of these richer structures has led to the recent rise and fall of some of the most famous conjectures in the history of combinatorics and representation theory: the Macdonald constant term conjectures, the shuffle... (more)
Organizing Committee
- Chris Bowman
- Nicolle Gonzalez
- Kyu-Hwan Lee
- nicolas Libedinsky
- Rosa Orellana
- Greta Panova
- Anne Schilling
- Jamie Vicary
- Adam Wagner
- Lauren Williams
Stochastic and Randomized Algorithms in Scientific Computing: Foundations and Applications
Jan 20 - Apr 24, 2026
In many scientific fields, advances in data collection and numerical simulation have resulted in large amounts of data for processing; however, relevant and efficient computational tools appropriate to analyze the data for further prediction and decision-making are still in their infancy. To tackle these challenges, the scientific research community has developed and used probabilistic tools in at least two different ways: first, stochastic methods to model and quantify these uncertainties in applications where there is underlying uncertainty; second, in applications that may be inherently deterministic but randomness is used as an algorithmic tool to drastically reduce computational costs while retaining the high accuracy of classic approaches.
Stochastic and randomized algorithms have already made a tremendous impact in areas such as numerical linear algebra (where matrix sketching and randomized approaches are used for efficient matrix approximations), Bayesian inverse problems... (more)
Organizing Committee
- Harbir Antil
- Julianne Chung
- Petros Drineas
- Youssef Marzouk
- Agnieszka Miedlar
- Arvind Krishna Saibaba