Past Event: Babuška Forum

Vignettes from Tensor Applications

Joe Kileel, University of Texas at Austin

Abstract

In this talk I will discuss high dimensional tensors, which can be thought of as higher order variants of matrices, and their low-rank decompositions.  I will report on applications, ranging from synchronization in computer vision to streaming in data analysis to 3D reconstruction of protein molecules, where different tensors arise and computing suitable low-rank decompositions of the tensors helps solve the problem at hand.  Along the way, I will highlight unique mathematical challenges that tensors present, through connections to randomized linear algebra and algebraic geometry.  No background on tensors is assumed.

Biography

Joe Kileel is an assistant professor in the Department of Mathematics at UT Austin and a principal faculty member at the Oden Institute since 2020.  He completed the Ph.D. in math at UC Berkeley in 2017 and then was a Simons postdoc at Princeton for 3 years.  Joe's research is in computational math, especially algebraic and geometric based approaches to data science.  He is a Sloan fellow in mathematics and has grants from the NSF and DOE.