Conference: ASE60: Synergistic Interactions between Theory and Computation

Massachusetts Institute Of Technology, Cambridge MA

Investigators

Abstract

The conference "Synergistic Interactions Between Theory and Computation" will be held at the Massachusetts Institute of Technology, Cambridge, MA, July 27-29, 2023. This meeting will focus on the nexus between theory and computation, particularly on computational "tricks'' that lead to deep theoretical insight, and on the use of deep theoretical results in fast, high-performing computation. Three specific areas of interest are random matrix theory, numerical linear algebra, and modern scientific computing. Established experts and promising junior researchers will present the latest advances and state-of-the-art techniques. We seek a fruitful exchange of ideas and the opportunity to interact across disciplinary boundaries. This interaction will be facilitated by the presence of numerous researchers who work at the intersection of two or more of these areas. In addition to the presentations, we have scheduled a poster session for young participants so they can publicize their results and receive feedback and guidance from the experts in the audience. Random matrix theory, with its myriad modern applications from randomized numerical linear algebra to signal processing and from optimization to machine learning, is informed and deepened by computational and numerics tricks of the sort that have yielded tridiagonal theoretical models for beta-ensembles and calculating limiting distributions via Kolmogorov's backward equation. On the other hand, the use of randomization in numerical linear algebra is a fast-growing subfield, due to the importance of working with extremely large datasets for which classical, deterministic algorithms are too slow. The new methods make extensive use of random matrix tools, while the need to properly address machine learning and optimization applications has in turn guided the modern development of random matrix theory. Finally, modern high-performance computing needs to deal with sparseness, structure, and fast and accurate approximation on the back end, and must allow the users to write code that reads like mathematics on the front end; modern programming languages like Julia are designed to allow for high-level mathematical abstraction with high-performance code. We aim to bring together the three aforementioned communities in order to foster interdisciplinary research and hopefully start and nurture collaborations among both experts and junior participants that will bear fruit in the years to come. The conference website is at: https://math.mit.edu/events/ase60celebration/ This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.