Geometry and Representation theory of tensors with applications

Joseph M. Landsberg (Texas A&M University)

These lectures will focus on the geometry and representation theory of tensors related to problems arising in computer science (complexity theory) quantum information theory and numerical analysis. I will introduce the following questions: complexity of matrix multiplication, formats for tensor decomposition, and the utility of shallow circuits. The origins of the questions as well as the necessary algebraic geometry (geometry of secant varieties and orbit closures) and representation theory (classical representation theory of the general linear group) to study these questions will be covered.