Seminars and Colloquia by Series

Friday, September 11, 2009 - 15:00 , Location: Skiles 269 , John Etnyre , Georgia Tech , Organizer:
We will discuss how to put a hyperbolic structure on various surface and 3-manifolds. We will being by discussing isometries  of hyperbolic space in dimension 2 and 3. Using our understanding of these isometries we will explicitly construct hyperbolic structures on all close surfaces of genus greater than one and a complete finite volume hyperbolic structure on the punctured torus. We will then consider the three dimensional case where we will concentrate on putting hyperbolic structures on knot complements. (Note: this is a 2 hr seminar)
Friday, September 11, 2009 - 15:00 , Location: Skiles 154 , Sergio Almada , Georgia Tech , Organizer:
The talk is based on the recent paper by M.Hairer, J.Mattingly, and M.Scheutzow with the same title.There are many Markov chains on infinite dimensional spaces whose one-step transition kernels are mutually singular when starting from different initial conditions. We give results which prove unique ergodicity under minimal assumptions on one hand and the existence of a spectral gap under conditions reminiscent of Harris' theorem. The first uses the existence of couplings which draw the solutions together as time goes to infinity. Such "asymptotic couplings" were central to recent work on SPDEs on which this work builds. The emphasis here is on stochastic differential delay equations.Harris' celebrated theorem states that if a Markov chain admits a Lyapunov function whose level sets are "small" (in the sense that transition probabilities are uniformly bounded from below), then it admits a unique invariant measure and transition probabilities converge towards it at exponential speed. This convergence takes place in a total variation norm, weighted by the Lyapunov function. A second aim of this article is to replace the notion of a "small set" by the much weaker notion of a "d-small set," which takes the topology of the underlying space into account via a distance-like function d. With this notion at hand, we prove an analogue to Harris' theorem, where the convergence takes place in a Wasserstein-like distance weighted again by the Lyapunov function. This abstract result is then applied to the framework of stochastic delay equations.
Friday, September 11, 2009 - 13:00 , Location: Skiles 255 , Ruoting Gong , Georgia Tech , , Organizer:
We develop a stochastic control system from a continuous-time Principal-Agent model in which both the principal and the agent have imperfect information and different beliefs about the project. We attempt to optimize the agent’s utility function under the agent’s belief. Via the corresponding Hamilton-Jacobi-Bellman equation we prove that the value function is jointly continuous and satisfies the Dynamic Programming Principle. These properties directly lead to the conclusion that the value function is a viscosity solution of the HJB equation. Uniqueness is then also established.
Thursday, September 10, 2009 - 15:00 , Location: Skiles 269 , Christian Houdré , Georgia Tech , Organizer:

Given a random word of size n whose letters are drawn independently
from an ordered alphabet of size m, the fluctuations of the shape of
the corresponding random RSK Young tableaux are investigated, when both
n and m converge together to infinity. If m does not grow too fast and
if the draws are uniform, the limiting shape is the same as the
limiting spectrum of the GUE. In the non-uniform case, a control of
both highest probabilities will ensure the convergence of the first row
of the tableau, i.e., of the length of the longest increasing
subsequence of the random word, towards the Tracy-Widom distribution.

Wednesday, September 9, 2009 - 14:00 , Location: Skiles 269 , Shannon Bishop , Georgia Tech , Organizer:
We describe how time-frequency analysis is used to analyze boundedness and Schatten class properties of pseudodifferential operators and Fourier integral operators.
Wednesday, September 9, 2009 - 13:00 , Location: Skiles 114 , Amy Novick-Cohen , Technion , Organizer: John McCuan
Grain boundaries within polycrystalline materials are known to be governed by motion by mean curvature. However, when the polycrystalline specimen is thin, such as in thin films, then the effects of the exterior surfaces start to play an important role. We consider two particularly simple geometries, an axi-symmetric geometry, and a half loop geometry which is often employed in making measurements of the kinetic coefficient in the motion by mean curvature equation, obtaining corrective terms which arise due to the coupling of grain boundaries to the exterior surface.   Joint work with Anna Rotman, Arkady Vilenkin & Olga Zelekman-Smirin
Series: Other Talks
Wednesday, September 9, 2009 - 13:00 , Location: Skiles 269 , John Etnyre , Ga Tech , Organizer: John Etnyre
In these talks we will introduced the basic definitions and examples of presheaves, sheaves and sheaf spaces. We will also explore various constructions and properties of these objects.
Wednesday, September 9, 2009 - 12:00 , Location: ISyE Executive Classroom , Steve Tyber , ISyE, Georgia Tech , Organizer: Annette Rohrs
In 1969, Gomory introduced the master group polyhedron for pure integer programs and derives the mixed integer cut (MIC) as a facet of a special family of these polyhedra. We study the MIC in this framework, characterizing both its facets and extreme points; next, we extend our results under mappings between group polyhedra; and finally, we conclude with related open problems. No prior knowledge of algebra or the group relaxation is assumed. Terminology will be introduced as needed. Joint work with Ellis Johnson.
Wednesday, September 9, 2009 - 12:00 , Location: Skiles 171 , Ernie Croot , School of Mathematics, Georgia Tech , , Organizer:
Additive combinatorics is a relatively new field, with many diverse and exciting research programmes.  In this talk I will discuss two of these programmes -- the continuing development of sum-product inequalities, and the unfolding progress on arithmetic progressions -- along with some new results proved by me and my collaborators.  Hopefully I will have time to mention some nice research problems as well.
Series: PDE Seminar
Tuesday, September 8, 2009 - 15:05 , Location: Skiles 255 , Konstantina Trivisa , University of Maryland, College Park , Organizer:
Multicomponent reactive flows arise in many practical applicationssuch as combustion, atmospheric modelling, astrophysics, chemicalreactions, mathematical biology etc. The objective of this work isto develop a rigorous mathematical theory based on the principles ofcontinuum mechanics. Results on existence, stability, asymptotics as wellas singular limits will be discussed.