Sophex Professor Introductions

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.