Programs & Events
Optimal Transport in Data Science
May 8 - 12, 2023
This workshop will focus on the intersection of mathematics, statistics, machine learning, and computation, when viewed through the lens of optimal transport (OT). Mathematical topics will include low-dimensional models for OT, linearizations of OT, and the geometry of OT including gradient flows and gradient descent in the space of measures. Relevant statistical topics will include reliable and efficient estimation of OT plans in high dimensions, the role of regularization in computing OT distances and plans, with applications to robust statistics, uncertainty quantification, and overparameterized machine learning. Computation will be a recurring theme of the workshop, with emphasis on the development of fast algorithms and applications to computational biology, high energy physics, material science, spatio-temporal modeling, natural language processing, and image processing.
Organizing Committee
- Shuchin Aeron
- Markos Katsoulakis
- James Murphy
- Luc Rey-Bellet
- Bjorn Sandstede
Dynamics, Rigidity and Arithmetic in Hyperbolic Geometry
May 15 - 19, 2023
This workshop focuses on the interplay between dynamics, rigidity, and arithmetic in hyperbolic geometry and related areas. There have been many striking developments in recent years, particularly related to totally geodesic submanifolds in both finite and infinite volume hyperbolic and even complex hyperbolic manifolds.
One aim of this workshop is to expose young researchers to these breakthroughs providing them with the necessary background from dynamics, and geometry to allow them to appreciate some of these recent advances, and prepare them to make new original contributions. For this purpose, we will have minicourses on "Arithmeticity, Superrigidity and totally geodesic manifolds", and "Rigidity and geodesic planes in infinite volume hyperbolic manifolds". These courses will be preceded by an introductory minicourse on Hyperbolic geometry. We will also have a minicourse on "Understanding of geodesic planes in hyperbolic 3-manifolds via computations and visualization". In... (more)
Organizing Committee
- David Fisher
- Dubi Kelmer
- Hee Oh
- Alan Reid
Tangled in Knot Theory
May 22 - 25, 2023
In spite of their omnipresence and importance, a number of questions about knots remain elusive. Addressing them solicits techniques from a range of mathematical disciplines at the interface of algebra, analysis, geometry, modeling, and low-dimensional topology. Some of the most exciting recent avenues of research include optimizing geometry, quantum knot invariants, and applications in material sciences, physics, and molecular biology.
This workshop emphasizes bridging the gap between theoretical, computational, and experimental approaches in knot theory and its applications, including artificial intelligence.
Organizing Committee
- Simon Blatt
- Eleni Panagiotou
- Philipp Reiter
- Radmila Sazdanovic
- Armin Schikorra
Mathematical and Scientific Machine Learning
Jun 5 - 9, 2023
MSML2023 is the fourth edition of a newly established conference, with emphasis on promoting the study of mathematical theory and algorithms of machine learning, as well as applications of machine learning in scientific computing and engineering disciplines. This conference aims to bring together the communities of machine learning, applied mathematics, and computational science and engineering, to exchange ideas and progress in the fast-growing field of scientific machine learning (SciML). The objective of this annual conference series is to promote the study of:
- Theory and algorithms of machine learning.
- Applications in scientific and engineering disciplines such as physics, chemistry, material sciences, fluid and solid mechanics, etc.
- To provide hands-on tutorials for students and new researchers in the field.
Previous MSML Conferences:
First MSML:Â
Organizing Committee
- Marta D'Elia
- George Karniadakis
- Siddhartha Mishra
- Themistoklis Sapsis
- Jinchao Xu
- Zhongqiang Zhang
Mathematical and Computational Biology
Jun 12 - 16, 2023
The field of mathematical and computational biology is rapidly growing. The most applicable computational models have been developed in collaboration between computational and life science researchers. This workshop aims to bring these groups together to facilitate and promote collaborations among them.
A mathematical model for one disease might also be useful in modeling another disease. Some researchers are working on theoretical mathematical & statistical problems related to biological and biomedical applications, while others are developing computational methodologies to address fundamental life science knowledge gaps.
This workshop fosters and features collaborations among these groups along with experimentalists and physicians. Theoreticians will be exposed to a variety of open biological questions in need of state-of-the-art and efficient mathematical methods. Computational scientists will learn about more robust and efficient methods that could be tailored to answer... (more)
Organizing Committee
- Wenrui Hao
- Panayotis Kevrekidis
- Natalia Komarova
- Marieke Kuijjer
- Olivia Prosper
- Leili Shahriyari
- Nathaniel Whitaker
Modern Applied and Computational Analysis
Jun 26 - 30, 2023
The mathematical and computational toolbox for modern experimental and engineering problems has become more diverse than ever before, with a flurry of new challenges in inverse problems and successful practical solutions that present further theoretical questions. In the spirit of the 2012 âChallenges in Geometry, Analysis, and Computation: High-Dimensional Synthesisâ workshop at Yale, the âModern Applied and Computational Analysisâ workshop will be a celebration of different perspectives on inverse problems, models, inference, and harmonic analysis and a debate about the challenges and opportunities in the next decade of applied analysis. The topics include inverse problems, randomized linear algebra, machine learning in applied analysis, and tensor networks.
The organizers would like to thank James Bremer, Ronald Coifman, Jingfang Huang, Peter Jones, Mauro Maggioni, Yair Minsky, Vladimir Rokhlin, Wilhelm Schlag, John Schotland, Amit Singer, Stefan Steinerberger, and Mark... (more)
Organizing Committee
- Anna Gilbert
- Roy Lederman
- Gilad Lerman
- Per-Gunnar Martinsson
- Andrea Nahmod
- Kirill Serkh
- Christoph Thiele
- Sijue Wu
Acceleration and Extrapolation Methods
Jul 24 - 28, 2023
Solving systems of nonlinear equations and optimization problems are pervasive issues throughout the mathematical sciences with applications in many areas. Acceleration and extrapolation methods have emerged as a key technology to solve these problems efficiently and robustly. The simple underlying idea of these methods is to recombine previous approximations in a sequence to determine the next term or approximation.
This approach has been applied repeatedly and from different angles to numerous problems over the last several decades. Important methods including epsilon algorithms and Anderson acceleration were introduced throughout the early and mid-20th century, and are now common in many applied fields including optimization, machine learning, computational chemistry, materials, and climate sciences. Within the last decade, theoretical advances on convergence, acceleration mechanisms, and the development of unified frameworks to understand these methods have come to light, yet our... (more)
Organizing Committee
- Hans De Sterck
- David Gardner
- Agnieszka Miedlar
- Sara Pollock
Spring 2021 Reunion Event
Jul 31 - Aug 18, 2023
The aim of this reunion meeting is to bring together the participants from the spring 2021 program “Combinatorial Algebraic Geometry” bringing together experts in both pure and applied parts of mathematics as well mathematical programmers, all working at the confluence of discrete mathematics and algebraic geometry, with the aim of creating an environment conducive to interdisciplinary collaboration.
Organizing Committee
- Anders Buch
- Melody Chan
- June Huh
- Thomas Lam
- Leonardo Mihalcea
- Sam Payne
- Lauren Williams
Computational Tools for Single-Cell Omics
Dec 11 - 15, 2023
Single-cell assays provide a tool for investigating cellular heterogeneity and have led to new insights into a variety of biological processes that were not accessible with bulk sequencing technologies. Assays generate observations of many different molecular types and a grand mathematical challenge is to devise meaningful strategies to integrate data gathered across a variety of different sequencing modalities. The first-order approach to do this is to analyze the projected data by clustering. Keeping more refined shape information about the data enables more meaningful and accurate analysis. Geometric methods include (i) Manifold learning: Whereas classical approaches (PCA, metric MDS) assume projection to a low-dimensional Euclidean subspace, manifold learning finds coordinates that lie on a not necessarily flat or contractible manifold. (ii) Topological data analysis: Algebraic topology provides qualitative descriptors of global shape. Integrating these descriptors across feature... (more)
Organizing Committee
- Elham Azizi
- Andrew Blumberg
- Lorin Crawford
- Bianca Dumitrascu
- Antonio Moretti
- Itsik Pe'er
Connecting Higher-Order Statistics and Symmetric Tensors
Jan 8 - 12, 2024
This workshop focuses on connections between higher-order statistics and symmetric tensors, and their applications to machine learning, network science, and other domains. Higher-order statistics refers to the study of correlations between three or more covariates. This is in contrast to the usual mean and covariance, which are based on one and two covariates.
Higher-order statistics are needed to characterize complex data distributions, such as mixture models. Symmetric tensors, meanwhile, are multi-dimensional arrays. They generalize covariance matrices and affinity matrices and can be used to represent higher-order correlations. Tensor decompositions extend matrix factorizations from numerical linear algebra to multilinear algebra. Recently tensor-based approaches have become more practical, due to the availability of bigger datasets and new algorithms.
The workshop brings together applied mathematicians, statisticians, probabilists, machine learning experts, and computational... (more)
Organizing Committee
- Joe Kileel
- Tamara Kolda
- Joao Pereira
Interacting Particle Systems: Analysis, Control, Learning and Computation
May 6 - 10, 2024
Systems of interacting particles or agents are studied across many scientific disciplines. They are used as effective models in a wide variety of sciences and applications, to represent the dynamics of particles in physics, cells in biology, people in urban mobility studies, but also, more abstractly in the context of mathematics, as sample particles in Monte Carlo simulations or parameters of neural networks in machine learning.
This workshop aims at bringing together researchers in analysis, computation, inference, control and applications, to facilitate cross-fertilization and collaborations.
Organizing Committee
- Jose Carrillo
- Katy Craig
- Massimo Fornasier
- Fei Lu
- Mauro Maggioni
- Kavita Ramanan
The Ceresa Cycle in Arithmetic and Geometry
May 13 - 17, 2024
In the 1980s, Ceresa exhibited one of the first naturally occurring examples of an algebraic cycle, the Ceresa cycle, which is in general homologically trivial but algebraically nontrivial. In the last few years, there has been a renewed interest in the Ceresa cycle, and other cycle classes associated to curves over arithmetically interesting fields, and their interactions with analytic, combinatorial, and arithmetic properties of those curves. We hope to capitalize on this momentum to bring together different communities of arithmetic geometers to fully explore explicit computations around the arithmetic and geometry of cycles when these various approaches are systematically combined.
Organizing Committee
- Daniel Corey
- Jordan Ellenberg
- Wanlin Li
- Daniel Litt
- Congling Qiu
- Padmavathi Srinivasan