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)

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.

The tentative schedule during the reunion event is:

• Thursday, June 9
• 9:00am-10:00am: Introduction
• 10:00am-11:00am: Coffee/social
• 11:00am-12:00pm: Panel #1: Academic panel
• 12:00am-2:00pm: Lunch
• 2:00pm-4:00pm: “Life after my Summer@ICERM” talks
• Friday, June 10
• 8:30am-10:00am: Coffee/social
• 10:00am-11:00pm: Panel #2: Industry... (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.

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 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)