Mathematics Graduate Students Organization

Seminar:

Date: February 9

M. Rojas:"Short Polynomials with Too Many Roots"

Abstract: Building polynomials that can be expressed compactly but have many roots is an amusing puzzle that has deep implications in complexity theory and arithmetic geometry. In this talk, we'll review a few tricks for building polynomials, with a very special recursive structure, that highlight some important conjectures connected to the P vs. NP Problem. No background in complexity theory or arithmetic geometry is assumed.

A. Comech:"Spectral stability of nonlinear wave equations"

Abstract: Many nonlinear field equations of Mathematical Physics are known to have localized oscillating solutions, similar to the Schroedinger eigenstates in Quantum Mechanics. When do such localized solutions exist? Do they describe some physical phenomena? Are they stable? Does every finite energy solution break into some combination of dispersing solitary waves? Are such solitary waves at least linearly stable, so that small perturbations do not grow exponentially in time?

In this talk, we will concentrate on the last question.