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.

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)

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 “Challenges in Geometry, Analysis, and Computation: High-Dimensional Synthesis” workshop at Yale, the “Modern Applied and Computational Analysis” 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)

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)

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: (more)

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.

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)

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.

The collection and analysis of large-scale population level and individual mobility and social mixing data raises fundamental ethical questions related to privacy, individual autonomy, consent, and the distribution of power in society. Balancing those concerns with the desires of public health researchers and policy makers to learn what they need from the data is a central challenge. Ethics is a fundamentally discursive discipline and useful guidance on any of the challenges mentioned above can only result from actively engaging with a variety of perspectives and openly discussing their implications for the design and implementation of the big data-driven methods and technologies used in public health research. At the same time, ethicists must gain substantive insight into the technical details of these means if they are to identify and discuss specific concerns, and provide targeted recommendations.

In this multidisciplinary workshop, we will brainstorm new ethical challenges... (more)

The aim of this reunion meeting is to bring together the participants from the Fall 2020 program “advances in computational relativity” to work in a focused way towards solving the most pressing mathematical modeling and numerical simulation issues facing the gravitational wave community, and cultivating new subfields within mathematics that focus on important, pressing issues related to gravitational waves as well as providing mathematicians with new questions and problems to explore.

The areas of focus will be: (i) mathematical and computational approaches for solving the source-free Einstein field equations (a nonlinear, coupled, hyperbolic-elliptic PDE system) including fundamental aspects of general relativity or alternative theories of gravity, (ii) mathematical and computational approaches for the Einstein field equations with matter and magnetic fields, as well as the multi-scale, multi-physics modeling challenges for such problems, and (iii) methods for the detection,... (more)

Interactive theorem proving software can check, manipulate, and generate proofs of mathematical statements, just as computer algebra software can manipulate numbers, polynomials, and matrices. Over the last few years, these systems have become highly sophisticated and have learnt a large amount of mathematics. One has to be open to the idea these systems will change the way mathematics is done, and how it is taught in universities.

At the ICERM workshop "Lean for the Curious Mathematician 2022", experts in the Lean theorem prover will explain how to do number theory, topology, geometry, analysis, and algebra in the Lean theorem prover. This will be accessible to mathematicians without a specific background in computer-proof systems. The material covered will range from undergraduate mathematics to modern research. Participants will be invited to begin formalizing mathematical objects from their own research.

Application Deadline: March 7, 2022.

A challenge for mathematical modeling, from toy dynamical system models to full weather and climate models, is applying data assimilation and dynamical systems techniques to models that exhibit chaos and stochastic variability in the presence of coupled slow and fast modes of variability. Recent collaborations between universities and government agencies in India and the United States have resulted in detailed observations of oceanic and atmospheric processes in the Bay of Bengal, the Arabian Sea, and the Indian Ocean, collectively observing many coupled modes of variability. One key target identified by these groups was the improvement of forecasts of variability of the summer monsoon, which significantly affects agriculture and water management practices throughout South Asia. The Monsoon Intraseasonal Oscillation is a northward propagating mode of precipitation variability and is one of the most conspicuous examples of coupled atmosphere-ocean processes during the summer... (more)