Fall 2011, Thursdays, Milner 216, 4:00-4:50 PM

Date: September 29

"  Mini-Talk "

* Prof. Harold Boas

* Prof. Gregory Berkolaiko


H. Boas: "Several complex reasons why a circle is not square"

: This mini-talk introduces some of the ideas of the theory of analytic functions of several complex variables in the context of a concrete geometric problem.

G. Berkolaiko: "Zeros of eigenfunctions"

I will discuss the subject of my recent research interest, the number and location of zeros of the eigenfunction of Laplace operator. The nodal lines and nodal domains make beautiful and mysterious pictures. There are many mathematical results about them but even more are open conjectures. Zeros of eigenfunctions can also be studied in the simplified setting of (discrete) graph eigenfunctions. I will explain a recent result connecting the number of zeros of graph eigenfunctions with the stability of the eigenvalue with respect to magnetic perturbation.