Seminars and Colloquia by Series

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.

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).

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.

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

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

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

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

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