Chris Peterson
Department of Mathematics
Colorado State University
 
Title: The Algebraic Geometry of Matrices
 
Abstract: This talk will cover some of the geometry underlying matrices and
tensors. An important tool that would occur naturally to an algebraic
geometer is the Segre Variety. Various Segre Varieties parametrize rank one
tensors of fixed shape. Secant Varieties to Segre Varieties parametrize
higher rank tensors. Singular Value Decomposition can be viewed as a method
of determining very special points on various Secant Varieties to various
Segre Varieties. There are many open problems related to the geometry of
higher Segre Varieties and their higher order secants. If time permits, some
of these open problems will be discussed.