CUR Decompositions and Applications
DateTuesday, March 19, 2019 - 12:30pm
AbstractThis talk will focus on an interesting matrix decomposition (CUR) which decomposes a matrix by selecting representative columns and rows from it. We give several equivalent formulations of this decomposition, and discuss randomized column and row sampling procedures which guarantee a valid CUR decomposition of a matrix is attained with high probability. We also discuss some perturbation results for the decomposition and illustrate some connections with applications including motion segmentation and facial recognition, as well as other data applications requiring dimensionality reduction as a first step.
Nick Ercolani, Department of Mathematics, University of Arizona
DateTuesday, March 26, 2019 - 12:30pm
AbstractThe Cross-Newell (CN) equation is an order parameter equation for modeling pattern formation in a broad range of extended physical systems. Ercolani, Indik, Newell and Passot (2000) developed a Legendre transform analysis for constructing explicit solutions of CN. In this talk we examine an extension of this method to the solution to mean curvature equations in both Riemannian and Lorentzian geometry. In the latter case we discover a connection to Born-Infeld theory. This is joint work with Patrick Shipman.