Colloquium: Ke Ye

Speaker: Ke Ye (L.E. Dickson Instructor, University of Chicago)

Title: Matrix decompositions

Abstract: Perhaps the most obvious motivation for the study of matrix decompositions is that one can use these decompositions to solve linear systems quickly. LU decomposition and QR decomposition are classical examples of matrix decompositions. We will discuss matrix decompositions for many other interesting matrices. For example, we will see that every matrix can be decomposed as the product of Toeplitz matrices and this result indicates that one has the hope to find a fast algorithm to solve linear systems. Tools we use are from algebraic geometry and algebraic group theory. (I will not assume audiences have backgrounds in algebraic geometry so I will review some basic facts first.)

Faculty host: Luke Oeding