
Date Time 
Location  Speaker 
Title – click for abstract 

09/19 4:00pm 
BLOC 624 
Eviatar Procaccia TAMU 
Introduction to SLE (SchrammLowner Evolution)
SLE is a family of random curves, which is proved to be the scaling limit of many discrete random interfaces, common in statistical physics. The study of SLE gave birth to beautiful techniques such as Smirnov's discrete holomorphic functions, and study of fractal dimension of random curves.
In this first talk I will introduce the subject of SLE, starting from a background of models in statistical physics (percolation, loop erased radnom walk, etc), and then continuing with the fantastic discoveries of Oded Schramm, Greg Lawler, Wendelin Werner, Steffen Rhode and others.


09/26 4:00pm 
BLOC 624 
Eviatar Procaccia TAMU 
Introduction to SLE (SchrammLowner Evolution) Part 2 

10/10 4:00pm 
BLOC 624 
Isaac Harris TAMU 
Some analytical tools for nonlinear eigenvalues applied to inverse scattering.
We will discuss some results pertaining to nonlinear eigenvalue problems and how they can be used to study the transmission eigenvalue problem that comes from inverse scattering. Transmission eigenvalue problems are a new class of eigenvalue problems that are nonselfadjoint and nonlinear (in the proper function spaces) which can not be handled by standard theory (such as the Hilbert–Schmidt theorem).


10/17 4:00pm 
BLOC 624 
Robert Rahm TAMU 
Asymptotic density of eigenvalues for 1 dimensional Schroedinger operators
Consider the Schr\odinger Equation
y''(x) + q(x)y(x) = \lambda y(x)
on $[0,\infty)$. We will initially assume only that q is nonnegative and increasing and \lim_{x\to\infty}q(x) = \infty but will later put some restrictive assumptions on it.
We will discuss the asymptotic density of eigenvalues of the equation. In particular, if N(T) is the number of eigenvalues less than T$ we will show:
N(T) = \int_{0}^{q^{1}(T)}\{Tq(x)\}^{1/2}dx + o(1). 

10/31 4:00pm 
BLOC 624 
Dean Baskin TAMU 
A brief introduction to resonances
Spectral theory for the Laplacian on compact manifolds gives you a discrete set of eigenvalues and an orthonormal basis of eigenfunctions. For noncompact problems, there is typically continuous spectrum and only finitely many eigenvalues. Is there anything resembling a discrete family of eigenvalues in this context? In some sense, the answer is yes: these are the resonances.
In this talk I will provide a brief introduction to the theory of resonances. I will provide some motivation for their study by working through the case of the onedimensional wave equation. I will then talk about resonances on Euclidean and hyperbolic spaces, where they can be calculated explicitly. Finally I will provide some discussion of how to define them in the case of potential scattering (and maybe some geometric scattering) via the analytic Fredholm theorem.
In a future talk I will use the explicit calculation of the resonances on hyperbolic space to calculate the asymptotic behavior of the wave equation on Minkowski space.


11/07 4:00pm 
BLOC 624 
Boris Hanin TAMU 
Introduction to the Quantum Hall Effect
The Quantum Hall effect concerns the low temperature behavior of many electrons confined to a two dimensional sample, such as the surface of a semiconductor, and subjected to a strong perpendicular magnetic field. In their seminal experiments in the early 1980’s, Von KlitzingDordaPepper and TsuiStormerGossard discovered that the socalled Hall conductance is robustly and precisely quantized. This lead to much to much work socalled topological phases of matter and topological insulators. In this talk, I will give a gentle introduction to the QHE, with a focus on the basic examples. I will then briefly describe what is known about the partition function for the simplest and most important QHE wavefunction introduced by Laughlin. I will end with an open question about partition functions for important generalizations of the Laughlin wavefunctions, called incompressible states boundaryless states. The analysis of these wavefunctions is thought to involve conformal field theory and topological recursion in more than one dimension. 