Mathematics Graduate Students Organization

Seminar:

Date: September 26

M. Anshelevich : "Polynomials and Random Matrices"

Abstract: I will briefly describe a specific project I hope to pursue with a student. The project involves random matrices and a deformation of the Hermite polynomials.

A. Comech: "Stability of solitary waves, spectra of operators, and complex analysis"

Abstract: Many equations of mathematical physics admit solutions which are time-periodic and localized in space; these are called solitary waves; they describe various physical phenomena.

To determine whether a solitary wave is stable, one linearizes the equation at this solitary wave and studies the spectrum of the resulting equation, trying to determine whether there are eigenvalues with positive real part (if so, small perturbations can grow exponentially, leading to instability of a solitary wave).

This work is based on some beautiful methods of complex/harmonic analysis; we will discuss some of the basic ones.