Seminars and Colloquia by Series

The number of vertices in a 6-critical graph is linear in its genus

Series
Graph Theory Seminar
Time
Thursday, September 2, 2010 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Luke Postle – Math, GT
A deep theorem of Thomassen shows that for any surface there are only finitely many 6-critical graphs that embed on that surface. We give a shorter self-contained proof that for any 6-critical graph G that embeds on a surface of genus g, that |V(G)| is at most linear in g. Joint work with Robin Thomas.

The Aleksandrov problem and optimal transport on $S^n$

Series
School of Mathematics Colloquium
Time
Thursday, September 2, 2010 - 11:00 for 1 hour (actually 50 minutes)
Location
249 Skiles
Speaker
Vladimir Oliker – Emory University –
The purpose of this talk is to describe a variational approach to the problemof A.D. Aleksandrov concerning existence and uniqueness of a closed convexhypersurface in Euclidean space $R^{n+1}, ~n \geq 2$ with prescribed integral Gauss curvature. It is shown that this problem in variational formulation is closely connected with theproblem of optimal transport on $S^n$ with a geometrically motivated cost function.

A Variational Estimate for Paraproducts

Series
Analysis Seminar
Time
Wednesday, September 1, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Yen Do – Georgia Tech
We show variational estimates for paraproducts, which can be viewed as bilinear generalizations of L\'epingle’s variational estimates for martingale averages or scaled families of convolution operators. The heart of the matter is the case of low variation exponents. Joint work with Camil Muscalu and Christoph Thiele.

Universality Limits for Random Matrices and orthogonal Polynomials

Series
Research Horizons Seminar
Time
Wednesday, September 1, 2010 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Doron Lubinsky – School of Mathematics - Georgia Tech
Orthogonal Polynomials play a key role in analysis of random matrices. We discuss universality limits in the so-called unitary case, showing how the universality limit reduces to an asymptotic involving reproducing kernels associated with orthogonal polynomials. As a consequence, we show that universality holds in measure for any compactly supported measure.

What is a tropical variety?

Series
Tropical Geometry Seminar
Time
Wednesday, September 1, 2010 - 10:05 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Josephine Yu – Georgia Tech
Tropical varieties are polyhedral objects that behave like algebraic varieties. They arise in a few different ways -- from polynomials with (max,+) operations, from study of Groebner bases, and from non-archimedean valuations of algebraic varieties. In this expository talk, I will introduce the tropical varieties of ideals in a polynomial ring from the point of view of (max,+) algebra and show how they are related to Groebner theory, Newton polytopes and their subdivisions. I will also discuss their properties and give some examples.

Small solutions of nonlinear Schrodinger equations near first excited states

Series
PDE Seminar
Time
Tuesday, August 31, 2010 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Professor Tai-Peng Tsai – Department of Mathematics, University of British Columbia –
Consider a nonlinear Schrodinger equation in $R^3$ whose linear part has three or more eigenvalues satisfying some resonance conditions. Solutions which are initially small in $H^1 \cap L^1(R^3)$ and inside a neighborhood of the first excited state family are shown to converge to either a first excited state or a ground state at time infinity. An essential part of our analysis is on the linear and nonlinear estimates near nonlinear excited states, around which the linearized operators have eigenvalues with nonzero real parts and their corresponding eigenfunctions are not uniformly localized in space. This is a joint work with Kenji Nakanishi and Tuoc Van Phan.The preprint of the talk is available at http://arxiv.org/abs/1008.3581

Spherical images of hypersurfaces

Series
Geometry Topology Seminar
Time
Monday, August 30, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Mohammad Ghomi – Ga Tech
We discuss necessary and sufficient conditions of a subset X of the sphere S^n to be the image of the unit normal vector field (or Gauss map) of a closed orientable hypersurface immersed in Euclidean space R^{n+1}.

Knots in overtwisted contact structures

Series
Geometry Topology Seminar
Time
Monday, August 23, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
John Etnyre – Ga Tech
The study of Legendrian and transversal knots has been an essential part of contact topology for quite some time now, but until recently their study in overtwisted contact structures has been virtually ignored. In the past few years that has changed. I will review what is know about such knots and discuss recent work on the "geography" and "botany" problem.

Computing transition paths for rare events

Series
Applied and Computational Mathematics Seminar
Time
Monday, August 23, 2010 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 002
Speaker
Maria Cameron – U Maryland

Please Note: I will propose two numerical approaches for minimizing the MFF. Approach I is good for high-dimensional systems and fixed endpoints. It is based on temperature relaxation strategy and Broyden's method. Approach II is good for low-dimensional systems and only one fixed endpoint. It is based on Sethian's Fast Marching Method.I will show the application of Approaches I and II to the problems of rearrangement of Lennard-Jones cluster of 38 atoms and of CO escape from the Myoglobin protein respectively.

At low temperatures, a system evolving according to the overdamped Langevin equation spends most of the time near the potential minima and performs rare transitions between them. A number of methods have been developed to study the most likely transition paths. I will focus on one of them: the MaxFlux Functional (MFF), introduced by Berkowitz in 1983.I will reintepret the MFF from the point of view of the Transition Path Theory (W. E & E. V.-E.) and show that the MaxFlux approximation is equivalent to the Eikonal Approximation of the Backward Kolmogorov Equation for the committor function.

Theory/ACO Seminar - Matching in Lopsided Bipartite Graphs and a New Matching Polytope

Series
Other Talks
Time
Friday, August 20, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Klaus 1447
Speaker
Kamal Jain – Microsoft Research, Redmond, WA

Please Note: This talk should be non-technical except the last few slides. The talk is based on a work done in collaboration with Denis Charles, Max Chickering, Nikhil Devanur, and Manan Sanghi, all from Microsoft.

Lopsided bipartite graphs naturally appear in advertising setting. One side is all the eyeballs and the other side is all the advertisers. An edge is when an advertiser wants to reach an eyeball, aka, ad targeting. Such a bipartite graph is lopsided because there are only a small number of advertisers but a large number of eyeballs. We give algorithms which have running time proportional to the size of the smaller side, i.e., the number of advertisers. One of the main ideas behind our algorithm and as well as the analysis is a property, which we call, monotonic quality bounds. Our algorithm is flexible as it could easily be adapted for different kinds of objective functions. Towards the end of the talk we will describe a new matching polytope. We show that our matching polytope is not only a new linear program describing the classical matching polytope, but is a new polytope together with a new linear program. This part of the talk is still theoretical as we only know how to solve the new linear program via an ellipsoid algorithm. One feature of the polytope, besides being intriguing, is that it has some notion of fairness built in. This is important for advertising since if an advertiser wants to reach 10 million users of type A or type B, advertiser won't necessarily be happy if we show the ad to 10 million users of type A only (though it fulfills the advertising contract in a technical sense).

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