# Spectral theory

Wednesday, April 26, 2017 - 10:30am - 11:30am

Braxton Osting (The University of Utah)

The spectrum of a Schroedinger operator with periodic potential generally consists of bands and gaps. In this talk, for fixed m, I'll consider the problem of maximizing the gap-to-midgap ratio for the m-th spectral gap over the class of potentials which have fixed periodicity and are pointwise bounded above and below. We prove that the potential maximizing the m-th gap-to-midgap ratio exists.

Thursday, December 15, 2016 - 1:30pm - 2:30pm

Christophe Hazard (École Nationale Supérieure de Techniques Avancées)

The purpose of this talk is to investigate the spectral effects of an interface between a usual dielectric and a negative-index material (NIM), that is, a dispersive material whose electric permittivity and magnetic permeability become negative in some frequency range.

Tuesday, December 13, 2016 - 1:30pm - 2:30pm

Jeremy Marzuola (University of North Carolina, Chapel Hill)

With Braxton Osting, we have considered spectral optimization of point set configurations for adjacency matrices and graphs on two dimensional surfaces. We study both tori and spheres. I will discuss our results, show several numerical simulations and review open problems and interesting directions to take this line of research.

Monday, December 12, 2016 - 9:00am - 10:00am

Patrick Joly (École Nationale Supérieure de Techniques Avancées)

We consider the propagation of waves in a periodic structure that can be represented as a infinite thick graph. We show that, provided that adequate boundary conditions are satisfied, the introduction of a lineic geometric perturbation of this reference structure can create the apparition of guided waves associated to frequencies inside any band gap of the periodic medium. The proof is based on an asymptotic analysis with respect to the thickness of the graph. We also explain how to compute such waves.

Monday, June 18, 2012 - 9:00am - 10:30am

Greg Anderson (University of Minnesota, Twin Cities)

The goals for the series of talks are as follows.

1. To fill in background for and to state the result of Haagerup, Schultz

and Thorbjornsen for polynomials in GUE matrices.

2. To prove the result taking care to explain the most important tricks,

e.g, the linearization trick.

3. To discuss extensions and related results in the literature.

4. To prove some extensions of HST to polynomials in Wigner matrices

(not the best or sharpest possible) using methods worth learning about in

1. To fill in background for and to state the result of Haagerup, Schultz

and Thorbjornsen for polynomials in GUE matrices.

2. To prove the result taking care to explain the most important tricks,

e.g, the linearization trick.

3. To discuss extensions and related results in the literature.

4. To prove some extensions of HST to polynomials in Wigner matrices

(not the best or sharpest possible) using methods worth learning about in

Friday, December 7, 2012 - 9:00am - 9:50am

Wenxian Shen (Auburn University)

The current talk is concerned with the spectral theory, in particular, the principal eigenvalue theory, of nonlocal dispersal operators with time

periodic dependence, and its applications. Nonlocal and

random dispersal operators are widely used to model diffusion systems

in applied sciences and share many properties.

There are also some essential differences between nonlocal and random dispersal operators, for example, a random dispersal operator always has a principal

eigenvalue, but a nonlocal dispersal operator may not

periodic dependence, and its applications. Nonlocal and

random dispersal operators are widely used to model diffusion systems

in applied sciences and share many properties.

There are also some essential differences between nonlocal and random dispersal operators, for example, a random dispersal operator always has a principal

eigenvalue, but a nonlocal dispersal operator may not