Algebraic geometry and the complexity of matrix multiplication

Theoretical computer science has given rise to new, exciting questions in algebraic geometry and representation theory. In this talkI will focus on the problem of matrix multiplication. It is generally conjectured by computer scientists that as n grows very large, it becomes almost as easy to multiply nxn matrices as it is to add them! After giving a brief history of the problem I will focus on algebraic geometry and representation theory relevant for the problem and conclude by discussing  recent work with A. Conner, A. Harper, and H. Huang.