Seminars and Colloquia by Series

Lecture series on the disjoint paths algorithm

Series
Graph Theory Seminar
Time
Monday, February 7, 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.

Braid groups and symplectic groups

Series
Geometry Topology Seminar
Time
Monday, February 7, 2011 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Dan Margalit – Georgia Tech
The braid group embeds in the mapping class group, and so the symplectic representation of the mapping class group gives rise to a symplectic represenation of the braid group. The basic question Tara Brendle and I are trying to answer is: how can we describe the kernel? Hain and Morifuji have conjectured that the kernel is generated by Dehn twists. I will present some progress/evidence towards this conjecture.

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.

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.

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.

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.

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.

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.

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.

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