Seminars and Colloquia Schedule

Lecture series on the disjoint paths algorithm

Series
Graph Theory Seminar
Time
Monday, January 31, 2011 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 168
Speaker
Paul Wollan – GT, Math and University of Rome
The k-disjoint paths problem takes as input a graph G and k pairs of vertices (s_1, t_1),..., (s_k, t_k) and determines if there exist internally disjoint paths P_1,..., P_k such that the endpoints of P_i are s_i and t_i for all i=1,2,...,k. While the problem is NP-complete when k is allowed to be part of the input, Robertson and Seymour showed that there exists a polynomial time algorithm for fixed values of k. The existence of such an algorithm is the major algorithmic result of the Graph Minors series. The original proof of Robertson and Seymour relies on the whole theory of graph minors, and consequently is both quite technical and involved. Recent results have dramatically simplified the proof to the point where it is now feasible to present the proof in its entirety. This seminar series will do just that, with the level of detail aimed at a graduate student level.

PDE Methods for Cardiovascular Treatment

Series
PDE Seminar
Time
Tuesday, February 1, 2011 - 10:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Prof. Suncica Canic – Department of Mathematics, University of Houston –
Mathematical modeling, analysis and numerical simulation, combined with imagingand experimental validation, provide a powerful tool for studying various aspects ofcardiovascular treatment and diagnosis. At the same time, problems motivated bycardiovascular applications give rise to mathematical problems whose studyrequires the development of sophisticated mathematical techniques. This talk willaddress two examples where such a synergy led to novel mathematical results anddirections. The first example concerns a mathematical study of the benchmarkproblem of fluid‐structure interaction (FSI) in blood flow. The resulting problem is anonlinear moving‐boundary problem coupling the flow of a viscous, incompressiblefluid with the motion of a linearly viscoelastic membrane/shell. An existence resultfor an effective, reduced model will be presented.The second example concerns a novel dimension reduction/multi‐scale approach tomodeling of endovascular stents as 3D meshes of 1D curved rods. The resultingmodel is in the form of a nonlinear hyperbolic network, for which no generalexistence results are available. The modeling background and the challenges relatedto the analysis of the solutions will be presented. An application to the study of themechanical properties of the currently available coronary stents on the US marketwill be shown.This talk will be accessible to a wide scientific audience.Collaborators include: Josip Tambaca (University of Zagreb, Croatia), Ando Mikelic(University of Lyon 1, France), Dr. David Paniagua (Texas Heart Institute), and Dr.Stephen Little (Methodist Hospital in Houston).

State Transitions and Feedback Loops in the Immune Response

Series
Job Candidate Talk
Time
Tuesday, February 1, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Peter Kim – University of Utah –
The immune system is a complex, multi-layered biological system, making it difficult to characterize dynamically. Perhaps, we can better understand the system’s construction by isolating critical, functional motifs. From this perspective, we will investigate two simple, yet ubiquitous motifs:state transitions and feedback regulation.Numerous immune cells exhibit transitions from inactive to activated states. We focus on the T cell response and develop a model of activation, expansion, and contraction. Our study suggests that state transitions enable T cells to detect change and respond effectively to changes in antigen levels, rather than simply the presence or absence of antigen. A key component of the system that gives rise to this change detector is initial activation of naive T cells. The activation step creates a barrier that separates the slow dynamics of naive T cells from the fast dynamics of effector T cells, allowing the T cell population to compare short-term changes in antigen levels to long-term levels. As a result, the T cell population responds to sudden shifts in antigen levels, even if the antigen were already present prior to the change. This feature provides a mechanism for T cells to react to rapidly expandingsources of antigen, such as viruses, while maintaining tolerance to constant or slowly fluctuating sources of stimulation, such as healthy tissue during growth.For our second functional motif, we investigate the potential role of negative feedback in regulating a primary T cell response. Several theories exist concerning the regulation of primary T cell responses, the most prevalent being that T cells follow developmental programs. We propose an alternative hypothesis that the response is governed by a feedback loop between conventional and adaptive regulatory T cells. By developing a mathematical model, we show that the regulated response is robust to a variety of parameters and propose that T cell responses may be governed by a simple feedback loop rather than by autonomous cellular programs.

Joint Athens-Atlanta Number Theory - Moments of zeta and L-functions

Series
Other Talks
Time
Tuesday, February 1, 2011 - 16:00 for 1 hour (actually 50 minutes)
Location
Emory University, Math and Science Center W201
Speaker
K. Soundararajan – Stanford University

If you wish to drive your own car and park, the closest parking deck<br />
is attached to the Oxford Rd Building. There will be a charge for<br />
parking, which is $6 for 2-3 hours. Once you have parked, exit the<br />
parking garage into the building and there will be an elevator to your<br />
right. Take the elevator to level 3. You should take a left out of<br />
the elevator and proceed through the glass doors into the courtyard<br />
area. The Mathematics and Science Center will be the building to your<br />
left.

An important theme in number theory is to understand the values taken by the Riemann zeta-function and related L-functions. While much progress has been made, many of the basic questions remain unanswered. I will discuss what is known about this question, explaining in particular the work of Selberg, random matrix theory and the moment conjectures of Keating and Snaith, and recent progress towards estimating the moments of zeta and L-functions.

Joint Athens-Atlanta Number Theory - Oscillatory integrals in analytic and adelic geometry

Series
Other Talks
Time
Tuesday, February 1, 2011 - 17:00 for 1 hour (actually 50 minutes)
Location
Emory University, Math and Science Center W201
Speaker
Yuri Tschinkel – New York University

If you wish to drive your own car and park, the closest parking deck is attached<br />
to the Oxford Rd Building. There will be a charge for parking, which is $6 for<br />
2-3 hours. Once you have parked, exit the parking garage into the building and<br />
there will be an elevator to your right. Take the elevator to level 3. You<br />
should take a left out of the elevator and proceed through the glass doors into<br />
the courtyard area. The Mathematics and Science Center will be the building to<br />
your left.

Oscillatory integrals arising as Fourier transforms of local and global height functions play an important role in the spectral analysis of height zeta functions. I will explain a general geometric technique which allows to evaluate such integrals. This is joint work with A. Chambert-Loir.

Exotic 4-manifolds

Series
Geometry Topology Student Seminar
Time
Wednesday, February 2, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Bulent Tosun – Georgia Tech
I will talk about rational blow down operation and give a quick exotic example.

The exotic world of 4-manifolds

Series
Research Horizons Seminar
Time
Wednesday, February 2, 2011 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
John Etnyre – Georgia Tech –
Four dimensions is unique in many ways. For examplen-dimensional Euclidean space has a unique smooth structure if andonly if n is not equal to four. In other words, there is only one wayto understand smooth functions on R^n if and only if n is not 4. Thereare many other way that smooth structures on 4-dimensional manifoldsbehave in surprising ways. In this talk I will discuss this and I willsketch the beautiful interplay of ideas (you got algebra, analysis andtopology, a little something for everyone!) that go into proving R^4has more that one smooth structure (actually it has uncountably manydifferent smooth structures but that that would take longer toexplain).

On eigenvalues of a sum of random matrices

Series
Job Candidate Talk
Time
Wednesday, February 2, 2011 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Vladislav Kargin – Department of Mathematics, Stanford University
Let H = A+UBU* where A and B are two N-by-N Hermitian matrices and U is a random unitary transformation. When N is large, the point measure of eigenvalues of H fluctuates near a probability measure which depends only on eigenvalues of A and B. In this talk, I will discuss this limiting measure and explain a result about convergence to the limit in a local regime.

Localization for the random displacement model

Series
Math Physics Seminar
Time
Wednesday, February 2, 2011 - 16:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Michael Loss – Georgia Tech –
I'll talk about recent work, jointly with J. Baker, F. Klopp, S. Nakamura and G. Stolz concerning the random displacement model. I'll outline a proof of localization near the edge of the deterministic spectrum. Localization is meant in both senses, pure point spectrum with exponentially decaying eigenfunctions as well as dynamical localization. The proof relies on a well established multiscale analysis and the main problem is to verify the necessary ingredients, such as a Lifshitz tail estimate and a Wegner estimate.

Decomposing an infinite matroid into its 3-connected minors

Series
Graph Theory Seminar
Time
Thursday, February 3, 2011 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Luke Postle – Math, GT
This will be a continuation from last week. We extend the theory of infinite matroids recently developed by Bruhn et al to a well-known classical result in finite matroids while using the theory of connectivity for infinitematroids of Bruhn and Wollan. We prove that every infinite connected matroid M determines a graph-theoretic decomposition tree whose vertices correspond to minors of M that are3-connected, circuits, or cocircuits, and whose edges correspond to 2-separations of M. Tutte and many other authors proved such a decomposition for finite graphs; Cunningham andEdmonds proved this for finite matroids and showed that this decomposition is unique if circuits and cocircuits are also allowed. We do the same for infinite matroids. The knownproofs of these results, which use rank and induction arguments, do not extend to infinite matroids. Our proof avoids such arguments, thus giving a more first principles proof ofthe finite result. Furthermore, we overcome a number of complications arising from the infinite nature of the problem, ranging from the very existence of 2-sums to proving the treeis actually graph-theoretic.

Scaling limit for the diffusion exit problem

Series
Dissertation Defense
Time
Thursday, February 3, 2011 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Sergio Angel Almada – School of Mathematics, Georgia Tech
A stochastic differential equation with vanishing martingale term is studied. Specifically, given a domain D, the asymptotic scaling properties of both the exit time from the domain and the exit distribution are considered under the additional (nonstandard) hypothesis that the initial condition also has a scaling limit. Methods from dynamical systems are applied to get more complete estimates than the ones obtained by the probabilistic large deviation theory. Two situations are completely analyzed. When there is a unique critical saddle point of the deterministic system (the system without random effects), and when the unperturbed system escapes the domain D in finite time. Applications to these results are in order. In particular, the study of 2-dimensional heteroclinic networks is closed with these results and shows the existence of possible asymmetries. Also, 1-dimensional diffusions conditioned to rare events are further studied using these results as building blocks.

Women's Group Meeting - Etiquette in Mathematics Discussion

Series
Other Talks
Time
Friday, February 4, 2011 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 257 (Math Lab)
Speaker
Group Discussion – School of Mathematics, Georgia Tech
All are welcome to discuss professionalism in math, including inviting a speaker, asking questions in talks, dress code at conferences and workshops, and sending polite requests to strangers. Some topics specifically pertaining to women's issues may be discussed. If possible, contact Becca Winarski (rwinarski@math.gatech.edu) if you plan to attend, however, note that everyone is welcome even if you do not respond.

A Riemannian geometry look at contact geometry

Series
Geometry Topology Working Seminar
Time
Friday, February 4, 2011 - 14:00 for 2 hours
Location
Skiles 269
Speaker
John Etnyre – Ga Tech
This will be the first of a two part lecture series investigating questions in contact geometry from the perspective of Riemannian geometry. Interesting questions in Riemannian geometry arising from contact geometry have a long and rich history, but there have been few applications of Riemannian geometry to contact topology. In these talks I will discuss basic connections between Riemannian and contact geometry and some applications of these connections. I will also discuss the "contact sphere theorem" that Rafal Komendarczyk, Patrick Massot and I recently proved as well as other results.

New Proofs in Graph Minors

Series
Combinatorics Seminar
Time
Friday, February 4, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Paul Wollan – Sapienza University of Rome
The graph minor structure theorem of Robertson and Seymour gives anapproximate characterization of which graphs do not contain some fixedgraph H as a minor. The theorem has found numerous applications,including Robertson and Seymour's proof of the polynomial timealgorithm for the disjoint paths problem as well as the proof ofWagner's conjecture that graphs are well quasi-ordered under the minorrelation. Unfortunately, the proof of the structure theorem isextremely long and technical. We will discuss a new proof whichgreatly simplifies the argument and makes the result more widelyaccessible. This is joint work with Ken-ichi Kawarabayashi.