Seminars and Colloquia Schedule

Absolutely continuous spectrum for random operators on certain graphs

Series
Job Candidate Talk
Time
Tuesday, January 21, 2014 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Christian Sadel – U. British Columbia, Vancouver –

Christian Sadel is a Mathematical Physicists with broad spectrum of competences, who has been working in different areas, Random Matrix Theory (with H. Schulz-Baldes), discrete Schrödinger operators and tree graphs (with A. Klein), cocycle theory (with S. Jitomirskaya & A. Avila), SLE and spectral theory (with B. Virag), application to Mott transports in semiconductors (with J. Bellissard).

When P. Anderson introduced a model for the electronic structure in random disordered systems in 1958, such as randomly doped semiconductors, the surprise was his claim of the possibility of absence of diffusion for the electron motion. Today this phenomenon is called Anderson's localization and corresponds to pure point spectrum with exponentially decaying eigenfunctions for certain random Schrödinger operators (or Anderson models). Mathematically this phenomenon is quite well understood.For dimensions d≥3 and small disorder, the existence of diffusion, i.e. absolutely continuous spectrum, is expected, but mathematically still an open problem. In 1994, A. Klein gave a proof for a.c. spectrum for theinfinite-dimensional, hyperbolic, regular tree. However, generalizations to other hyperbolic trees and so-called "tree-strips" have only been made only in recent years. In my talk I will give an overview of the subject and these recent developments.

Blowup criterion for the strong solutions to 3D incompressible Navier-Stokes equations in BMO^{-s} spaces

Series
PDE Seminar
Time
Tuesday, January 21, 2014 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jianli Liu – Shanghai Unversity
This talk gives a blowup criteria to the incompressible Navier-Stokes equations in BMO^{-s} on the whole space R^3, which implies the well-known BKM criteria and Serrin criteria. Using the result, we can get the norm of |u(t)|_{\dot{H}^{\frac{1}{2}}} is decreasing function. Our result can obtained by the compensated compactness and Hardy space result of [6] as well as [7].

Dynamics of a delay equation with two state dependent delays

Series
CDSNS Colloquium
Time
Wednesday, January 22, 2014 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Renato Calleja – IIMAS UNAM
We present a numerical study of the dynamics of a state-dependent delay equation with two state dependent delays that are linear in the state. In particular, we study some of the the dynamical behavior driven by the existence of two-parameter families of invariant tori. A formal normal form analysis predicts the existence of torus bifurcations and the appearance of a two parameter family of stable invariant tori. We investigate the dynamics on the torus thought a Poincaré section. We find some boundaries of Arnold tongues and indications of loss of normal hyperbolicity for this stable family. This is joint work with A. R. Humphries and B. Krauskopf.

Intra-Host Adaptation and Antigenic Cooperation of RNA Viruses: Modeling and Computational Analysis.

Series
Mathematical Biology Seminar
Time
Wednesday, January 22, 2014 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles Bld Room 005
Speaker
Pavel Skums – CDC
Understanding the mechanisms responsible for the establishment of chronic viral infections is critical to the development of efficient therapeutics and vaccines against highly mutable RNA viruses, such as Hepatitis C (HCV). The mechanism of intra-host viral evolution assumed by most models is based on immune escape via random mutations. However, continuous immune escape does not explain the recent observations of a consistent increase in negative selection during chronic infection and long-term persistence of individual viral variants, which suggests extensive intra-host viral adaptation. This talk explores the role of immune cross-reactivity of viral variants in the establishment of chronic infection and viral intra-host adaptation. Using a computational prediction model for cross-immunoreactivity of viral variants, we show that the level of HCV intra-host adaptation correlates with the rate of cross-immunoreactivity among HCV quasispecies. We analyzed cross-reactivity networks (CRNs) for HCV intra-host variants and found that the structure of CRNs correlates with the type and strength of selection in viral populations. Based on those observations, we developed a mathematical model describing the immunological interaction among RNA viral variants that involves, in addition to neutralization, a non-neutralizing cross-immunoreactivity. The model describes how viral variants escape immune responses and persist, owing to their capability to stimulate non-neutralizing immune responses developed earlier against preceding variants. The model predicts the mechanism of antigenic cooperation among viral variants, which is based on the structure of CRNs. In addition, the model allows to explain previously observed and unexplained phenomenon of reappearance of viral variants: for some chronically infected patients the variants sampled during the acute stage are phylogenetically distant from variants sampled at the earlier years of infection and intermixed with variants sampled 10-20 years later. (Joint work with Y. Khudyakov, Z.Dimitrova, D.Campo and L.Bunimovich)

Two Weight Inequality for the Hilbert Transform

Series
Research Horizons Seminar
Time
Wednesday, January 22, 2014 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dr. Lacey – School of Math
Beginning with the Cauchy formula, we introduce the Poisson average, and the Carleson embeding theorem. From there, recent weighted estimates for the Hilbert and Cauchy transforms can be introduced.

Universality in Random Normal Matrices

Series
Analysis Seminar
Time
Wednesday, January 22, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dr. Roman Riser – ETH, Zurich
In the beginning, the basics about random matrix models and some facts about normal random matrices in relation with conformal map- pings will be explained. In the main part we will show that for Gaussian random normal matrices the eigenvalues will fill an elliptically shaped do- main with constant density when the dimension n of the matrices tends to infinity. We will sketch a proof of universality, which is based on orthogonal polynomials and an identity which plays a similar role as the Christoffel- Darboux formula in Hermitian random matrices. Especially we are interested in the density at the boundary where we scale the coordinates with n^(-1/2). We will also consider the off-diagonal part of the kernel and calculate the correlation function. The result will be illustrated by some graphics.

Towards the control of multiscale stochastic systems

Series
Job Candidate Talk
Time
Thursday, January 23, 2014 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Molei Tao – Courant Institute, NYU
Motivated by rich applications in science and engineering, I am interested in controlling systems that are characterized by multiple scales, geometric structures, and randomness. This talk will focus on my first two steps towards this goal. The first step is to be able to simulate these systems. We developed integrators that do not resolve fast scales in these systems but still capture their effective contributions. These integrators require no identification of underlying slow variables or processes, and therefore work for a broad spectrum of systems (including stiff ODEs, SDEs and PDEs). They also numerically preserve intrinsic geometric structures (e.g., symplecticity, invariant distribution, and other conservation laws), and this leads to improved long time accuracy. The second step is to understand what noises can do and utilize them. We quantify noise-induced transitions by optimizing probabilities given by Freidlin-Wentzell large deviation theory. In gradient systems, transitions between metastable states were known to cross saddle points. We investigate nongradient systems, and show transitions may instead cross unstable periodic orbits. Numerical tools for identifying periodic orbits and for computing transition paths are proposed. I will also describe how these results help design control strategies.

Blsachke Products

Series
Analysis Working Seminar
Time
Friday, January 24, 2014 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Philip Benge – School of Math
Philip will be presenting topics (and leading discussion on those topics) from Chapter 2 Section 2 of Bounded Analytic Functions.

New model for cell phone signal problem

Series
SIAM Student Seminar
Time
Friday, January 24, 2014 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Li Wuchen – School of Mathematics, Georgia Tech
We introduce a new model for cell phone signal problem, which is stochastic van der Pol oscillator with condition that ensures global boundedness in phase space and keeps unboundedness for frequency. Also we give a new definition for stochastic Poincare map and find a new approximation to return time and point. The new definition is based on the numerical observation. Also we develop a new approach by using dynamic tools, such as method of averaging and relaxation method, to estimate the return time and return point. Thus we can show that the return time is always not Gaussian and return point's distribution is not symmetric under certain section.

Atlanta Lecture Series in Combinatorics and Graph Theory XI

Series
Other Talks
Time
Saturday, January 25, 2014 - 09:00 for 8 hours (full day)
Location
Georgia State University, Room 150, College of Education, 30 Pryor Street, Atlanta, GA
Speaker
Alexander Schrijver – Centrum Wiskunde & Informatica, Amsterdam
Emory University, Georgia Tech and Georgia State University, with support from the National Science Foundation and the National Security Agency, will continue the series of mini-conferences and host a series of 9 new mini-conferences from 2013-2016. The 11th of these mini-conferences will be held at Georgia State University from January 25-26, 2014. The conferences will stress a variety of areas and feature one prominent researcher giving 2 fifty minute lectures and 4 outstanding researchers each giving one fifty minute lecture. There will also be several 25 minute lecturers by younger researchers or graduate students. For more details, see the schedule