Convex matrix optimization problems with low-rank solutions play a fundamental role in signal processing, statistics, and related disciplines. These problems are difficult to solve because of the cost of maintaining the matrix decision variable, even though the low-rank solution has few degrees of freedom. This talk presents an algorithm that provably solves these problems using optimal storage. The algorithm produces high-quality solutions to large problem instances that, previously, were intractable. Joint work with Volkan Cevher, Roarke Horstmeyer, Quoc Tran-Dinh, Madeleine Udell, and Alp Yurtsever. Bio Joel A. Tropp is Steele Family Professor of Applied & Computational Mathematics at the California Institute of Technology. He earned the Ph.D. degree in Computational Applied Mathematics from the University of Texas at Austin in 2004. His research centers on signal processing, numerical analysis, and random matrix theory. Prof. Tropp won a PECASE in 2008, and he has received society best paper awards from SIAM in 2010, EUSIPCO in 2011, and IMA in 2015. He has also been recognized as a Highly Cited Researcher in Computer Science each year from 2014–2017.