Randomized Methods for Very Large-Scale Linear Algebra

Registration for this lecture will close at 2 p.m. the day of the event. Review the complete list of entrance requirements below.

This lecture is part of the Randomness Presidential Lecture Series in Mathematics and Computer Science.

At the core of many computational simulations of physical systems lies a linear algebraic problem, such as a system of linear equations to be solved or an eigenvalue problem. Similar problems also arise throughout computational statistics and data science. Because such computations are often the most computationally expensive part of a simulation, they frequently determine both the simulation’s feasibility and the level of physical detail it can achieve.

In this Presidential Lecture, Per-Gunnar Martinsson will describe how ideas from random matrix theory and high-dimensional probability have, in recent years, enabled a new generation of algorithms that are far faster than traditional deterministic methods and have enabled simulations of problems once considered intractable. One of the most important features of these randomized methods is that they require very little data movement, making them especially well-suited to modern computing hardware. The lecture will present methods for low-rank approximation, for solving linear systems, and for constructing highly accurate compressed representations of continuum operators, including solution operators for elliptic partial differential equations, Dirichlet-to-Neumann maps and time-evolution operators.

Martinsson is a professor of mathematics and the W. A. "Tex" Moncrief, Jr. Endowed Chair in Simulation-Based Engineering and Sciences at the University of Texas at Austin, as well as deputy director of the university’s Oden Institute for Computational Engineering and Sciences. He earned a Ph.D. in computational and applied mathematics from UT Austin in 2002 after receiving degrees in engineering physics and mathematics from Chalmers University of Technology in Sweden. His research focuses on the development of fast algorithms for scientific computing and data science, including randomized linear algebra, fast solvers for partial differential equations and structured matrix computations. He is a Society for Industrial and Applied Mathematics Fellow and a 2017 Germund Dahlquist Prize recipient.

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SCHEDULE

Doors open: 5:30 p.m. (No entrance before 5:30 p.m.)

Lecture: 6:00 p.m.–7:00 p.m. (Admittance closes at 6:20 p.m.)

The Gerald D. Fischbach Auditorium complies with the Americans with Disabilities Act and offers accessible seating to visitors with special access needs.

Presidential Lectures are free public colloquia at the Simons Foundation centered on four main themes: Biology, Physics, Mathematics and Computer Science, and Neuroscience and Autism Science. These curated, high-level scientific talks feature leading scientists and mathematicians and are intended to foster discourse and drive discovery among the broader NYC-area research community. We invite anyone interested in the topic to join us for this weekly lecture series.