Seminars and Colloquia by Series

The Sherrington-Kirkpatrick model and its diluted version (**Cancelled due to inclement weather**)

Series
School of Mathematics Colloquium
Time
Thursday, February 13, 2014 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Dmitry Panchenko – Texas A&M University
Abstract: I will talk about two types of random processes -- the classical Sherrington-Kirkpatrick (SK) model of spin glasses and its diluted version. One of the main goals in these models is to find a formula for the maximum of the process, or the free energy, in the limit when the size of the system is getting large. The answer depends on understanding the structure of the Gibbs measure in a certain sense, and this structure is expected to be described by the so called Parisi solution in the SK model and Mézard-Parisi solution in the diluted SK model. I will explain what these are and mention some results in this direction.

Overview of Yamabe problem

Series
Geometry Topology Student Seminar
Time
Wednesday, February 12, 2014 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006.
Speaker
Amey Kaloti – Georgia Tech.
We will give an overview of ideas that go into solution of Yamabe problem: Given a compact Riemannian manifold (M,g) of dimension n > 2, find a metric conformal to g with constant scalar curvature.

Variational model and Imaging applications

Series
Research Horizons Seminar
Time
Wednesday, February 12, 2014 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Prof. Kang – School of Math
This talk is an introduction to mathematical approaches to image processing: using variational approaches and PDE based method. Various problems and a few different approaches will be introduced.

Convex cocompactness in mapping class groups via quasiconvexity in right-angled Artin groups

Series
Geometry Topology Seminar
Time
Monday, February 10, 2014 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Johanna Mangahas – U at Buffalo
I'll talk about joint work with Sam Taylor. We characterize convex cocompact subgroups of mapping class groups that arise as subgroups of specially embedded right-angled Artin groups. We use this to construct convex cocompact subgroups of Mod(S) whose orbit maps into the curve complex have small Lipschitz constants.

Modeling inoculum dose dependent patterns of acute virus infections

Series
Mathematical Biology Seminar
Time
Monday, February 10, 2014 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Professor Andeas Handel – Department of Epidemiology and Biostatistics, College of Public Health, UGA –
Inoculum dose, i.e. the number of pathogens at the beginning of an infection, often affects key aspects of pathogen and immune response dynamics. These in turn determine clinically relevant outcomes, such as morbidity and mortality. Despite the general recognition that inoculum dose is an important component of infection outcomes, we currently do not understand its impact in much detail. This study is intended to start filling this knowledge gap by analyzing inoculum dependent patterns of viral load dynamics in acute infections. Using experimental data for adenovirus and infectious bronchitis virus infections as examples, we demonstrate inoculum dose dependent patterns of virus dynamics. We analyze the data with the help of mathematical models to investigate what mechanisms can reproduce the patterns observed in experimental data. We find that models including components of both the innate and adaptive immune response are needed to reproduce the patterns found in the data. We further analyze which types of innate or adaptive immune response models agree with observed data. One interesting finding is that only models for the adaptive immune response that contain growth terms partially independent of viral load can properly reproduce observed patterns. This agrees with the idea that an antigen-independent, programmed response is part of the adaptive response. Our analysis provides useful insights into the types of model structures that are required to properly reproduce observed virus dynamics for varying inoculum doses.

Homogeneous Adjacency Spectra of Random and Complete Hypergraphs

Series
Combinatorics Seminar
Time
Friday, February 7, 2014 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Josh Cooper – University of South Carolina
Abstract: There has been a recent flurry of interest in the spectral theory of tensors and hypergraphs as new ideas have faithfully analogized spectral graph theory to uniform hypergraphs. However, even in their simplest incarnation -- the homogeneous adjacency spectrum -- a large number of seemingly basic questions about hypergraph spectra remain out of reach. One of the problems that has yet to be resolved is the (asymptotically almost sure) spectrum of a random hypergraph in the Erd\H{o}s-R\'{e}nyi sense, and we still don't know the spectrum of complete hypergraphs (other than a kind of implicit description for 3-uniform). We introduce the requisite theoretical framework and discuss some progress in this area that involves tools from commutative algebra, eigenvalue stability, and large deviations.

A Thouless formula for quasi-periodic long-range Schrödinger operators

Series
CDSNS Colloquium
Time
Friday, February 7, 2014 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 06
Speaker
Alex Haro – Univ. of Barcelona
This talk is devoted to quasi-periodic Schrödinger operators beyond theAlmost Mathieu, with more general potentials and interactions. The linksbetween the spectral properties of these operators and the dynamicalproperties of the associated quasi-periodic linear skew-products rule thegame. In particular, we present a Thouless formula and some consequencesof Aubry duality. This is a joint work with Joaquim Puig~

Information Relaxation and Duality in Stochastic Optimal Control

Series
Stochastics Seminar
Time
Thursday, February 6, 2014 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Enlu Zhou – ISYE Gatech
In this talk, I will talk about some recent research development in the approach of information relaxation to explore duality in Markov decision processes and controlled Markov diffusions. The main idea of information relaxation is to relax the constraint that the decisions should be made based on the current information and impose a penalty to punish the access to the information in advance. The weak duality, strong duality and complementary slackness results are then established, and the structures of optimal penalties are revealed. The dual formulation is essentially a sample path-wise optimization problem, which is amenable to Monte Carlo simulation. The duality gap associated with a sub-optimal policy/solution also gives a practical indication of the quality of the policy/solution.

Carleson and Reverse Carleson measures

Series
Analysis Seminar
Time
Wednesday, February 5, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Bill Ross – University of Richmond
This will be a survey talk on the ongoing classification problem for Carleson and reverse Carleson measures for the de Branges-Rovnyak spaces. We will relate these problems to some recent work of Lacey and Wick on the boundedness of the Cauchy transform operator.

Knot Contact Homology

Series
Geometry Topology Student Seminar
Time
Wednesday, February 5, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jamie Conway – GeorgiaTech
Knot Contact Homology is a powerful invariant assigning to each smooth knot in three-space a differential graded algebra. The homology of this algebra is in general difficult to calculate. We will discuss the cord algebra of a knot, which allows us to calculate the grading 0 knot contact homology. We will also see a method of extracting information from augmentations of the algebra.

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