Tuesday, April 28, 2015, 4pm
Joel Tropp, Caltech.
Applied Random Matrix Theory
Abstract: Random matrices now play a role in many areas of theoretical, applied, and computational mathematics. Therefore, it is desirable to have tools for studying random matrices that are flexible, easy to use, and powerful. Over the last fifteen years, researchers have developed a remarkable family of results, called matrix concentration inequalities, that balance these criteria.
This talk offers an invitation to the field of matrix concentration inequalities. The presentation begins with some history of random matrix theory, and it introduces an important probability inequality for scalar random variables. It describes a flexible model for random matrices that is suitable for many problems, and it discusses one of the most important matrix concentration results, the matrix Bernstein inequality. The talk concludes with some applications drawn from algorithms, combinatorics, statistics, signal processing, scientific computing, and beyond.
Bio: Joel A. Tropp is Professor of Applied & Computational Mathematics at the California Institute of Technology. He earned his PhD degree in Computational Applied Mathematics from the University of Texas at Austin in 2004. Dr. Tropp’s work lies at the interface of applied mathematics, electrical engineering, computer science, and statistics. This research concerns the theoretical and computational aspects of data analysis, sparse modeling, randomized linear algebra, and random matrix theory. Dr. Tropp has received several major awards for young researchers, including the 2007 ONR Young Investigator Award and the 2008 Presidential Early Career Award for Scientists and Engineers. He is also the winner of the 6th Vasil A. Popov prize and the 2011 Monroe H. Martin prize.