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.

The goal of this workshop is to introduce participants to interdisciplinary collaborations and conversations in network science that are advancing social justice research through the study of social structures. This workshop will bring together social scientists, digital humanists, computational scientists, and mathematicians with experience in network theory and network analysis in social systems. This workshop will also showcase how mixed methods research (which combines qualitative analysis and quantitative analysis) with multidisciplinary perspectives leads to deeper insights and more ethical and responsible approaches. Workshop organizers will lead tutorials in the mathematics of network theory, finding and working with network data, and qualitative methods for networks in the social sciences. We will emphasize and showcase the use of a critical lens throughout the process, from model building to data collection and analysis, connecting us to a broader dialogue about algorithmic... (more)

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)

The Summer@ICERM faculty advisers will present a variety of research projects on the combinatorics of parking functions. This overarching theme will allow participants to study and analyze parking functions by leveraging computational techniques and theory. Faculty will also guide the development of open-source computational tools for analyzing parking functions and their statistics, with time devoted to creating a database of parking functions and their generalizations.

Throughout the eight-week program, 18-22 students will work on their projects in groups of two to four, supervised by faculty advisors and aided by teaching assistants. Students will meet daily, give regular talks about their findings, attend mini-courses, guest talks, and professional development seminars, and will acquire skills in free software development. Students will learn how to collaborate mathematically, working closely in their teams to write up their research into a paper.

The Social Justice and Data Science Summer Research Program at ICERM aims to increase interest, research training, and capacity for data science for social justice, and to develop both quantitative and qualitative approaches to those professional practices that call for community engagement, critical inquiry, and interdisciplinary cooperation. In order to advance the mathematics community's understanding of the complexity of computational social justice work, the program will have four emphasis areas (1) networks, (2) policy, (3) education and (4) community-driven research. While the program itself is broadly computational and applied mathematics, researchers with expertise and interests in network science and analysis, open science and data, and computer science are particularly encouraged to apply. As a new field emerges at the face of computational and applied mathematics and social justice, this requires new methods for working across community lines. The organizers are committed... (more)

The 2020 Summer@ICERM program, held virtually due to the COVID-19 pandemic, involved 19 students from across the US in research projects investigating large-scale linear algebra, model reduction, randomized algorithms, and deep learning. Since the program, some students have begun successful technical careers in mathematics and computation, and some have matriculated in graduate school programs. This in-person reunion event, to be held from June 9-10, 2022 at ICERM, aims to rekindle professional relationships and possibly spark new directions for research.

Mathematical models arising from scientific applications frequently have a large number of degrees of freedom, and modern observational or empirical datasets have high-dimensional features. Such high-dimensional realities from either simulation or experimental data makes direct computational analysis, compression, and/or probing tasks such as outer-loop optimization, design, and/or uncertainty quantification computationally infeasible. One paradigm for addressing such a challenge is mathematics-based model reduction, which aims to find and exploit low-dimensional structure in high-dimensional models to generate a computationally efficient emulator, often with provable accuracy guarantees. A complementary class of approaches is found in low-rank approximation and statistics where data reduction techniques can efficiently explore and mine parsimonious summarizations of high-dimensional datasets. One major goal of the Spring 2020 program, and the foundational theme for this proposed... (more)

With the substantial recent progress in connectomics, the study of comprehensive maps of nervous systems, much more is known about the connectivity structure of brains. This has led to a multitude of new questions about the relationship between connectivity patterns, neural dynamics and brain function, many of which lead to new mathematical problems in graph theory and dynamics on graphs. The goal of this workshop is to bring together a broad range of researchers from neuroscience, physics, mathematics, and computer science to discuss new challenges in this emergent field and promote new collaborations.

This workshop is fully funded by a Simons Foundation Targeted Grant to Institutes.

This two-day interactive and research-oriented workshop brings together researchers and leaders at the interface of general relativity, quantum gravity, and mathematics with a focus on Chern-Simons Classical and Quantum Gravity. A main goal of the workshop is to find new synergies across sub-disciplines with an eye towards observational signatures.