Title: Controlling Eigenvalues (at least in theory)
Speaker: Adam Marcus
Speaker Info: Yale University
The importance of understanding eigenvalues has exploded in recent decades, far faster than the development of techniques available for gaining such understanding. As a result, a number of areas found themselves plagued by similar questions that none were equipped to handle. In this talk, I will introduce a new technique we call the `method of interlacing polynomials' that we have used to break through a number of these barriers, most notably in a proof of the Kadison--Singer conjecture. I will motivate the technique, show how it was used in the recent proof of KS and then discuss possible relationships with a number of areas of mathematics. The talk will be accessible to a general mathematical audience, including graduate students and advanced undergraduates.Date: Wednesday, November 19, 2014
All results represent joint work with Dan Spielman (Yale) and Nikhil Srivastava (Berkeley).