Over the past four decades, demands of resolution and fidelity have driven the performance of simulations of first-principles mathematical models in science and engineering from MegaFlop/s to ExaFlop/s, and their datasets from MegaBytes to ExaBytes. Over the most recent decade, the application of machine learning to science and engineering systems has created a similar demand for performance and associated storage. Increasingly, the same science or engineering application is more effectively addressable by simulation and machine learning working in tandem than by either alone, resulting in a confluence of two formerly distinct research communities. This workshop aims to capitalize by highlighting opportunities for cross-fertilization in both directions.

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This workshop encompasses three major aspects of computation within representation theory and algebraic combinatorics. One concerns the development of efficient algorithms to compute important quantities in order to understand and classify them better. This is closely related to understanding what optimality we could expect and in particular the computational complexity aspects of those problems. Computational complexity class can also be used to understand the existence of combinatorial interpretations, particularly for major structure constants lacking positive formulas like Kronecker and plethysm coefficients. On the other hand, representation theory has seen important applications within computational complexity theory in the context of geometric complexity theory and quantum information theory. In addition to these topics, workshop participants will discuss the collection of “experimental” data, which helps formulate conjectures, find counterexamples and understand the behavior for several problems.

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This workshop focuses on advancing the mathematical understanding of fluid dynamics, particularly the intricate phenomenon of turbulence. It aims to explore recent breakthroughs in the analysis of fluid equations, such as the Navier-Stokes and Euler equations, addressing fundamental questions of well-posedness, singularity formation, stability, and anomalous energy dissipation. Participants will explore cutting-edge mathematical techniques, including singularity formation, anomalous dissipation, convex integration, optimal transport, and

regularity theory for partial differential equations.

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Webs are diagrammatic tools for representing complex calculations graphically. These diagrams first arose from the representation theory of classical groups, and they have since become important in disparate areas of mathematics such as representation theory, topology, and algebraic geometry. This workshop is motivated by the belief that webs may serve as a nexus for disparate communities of mathematicians to meet. This includes not only researchers in algebraic combinatorics, Schubert calculus, and representation theory, but also those in algebraic geometry, topology and knot theory. The goal of this workshop is to bring together experts from these communities and spread knowledge of recent developments and perspectives on our shared interest: webs. The program will also allow distinct research groups to share current code functionality, as well as future needs and desires, with an aim towards building collaborative and open-source computing capabilities.

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