Seminars and Colloquia by Series

Convergence to equilibrium for a thin-film equation

Series
Math Physics Seminar
Time
Wednesday, February 23, 2011 - 16:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Professor Almut BurchardDepartment of Mathematics, University of Toronto
I will describe recent work with Marina Chugunovaand Ben Stephens on the evolution of a thin-filmequation that models a "coating flow" on a horizontalcylinder. Formally, the equation defines a gradientflow with respect to an energy that controls theH^1-norm.We show that for each given mass there exists aunique steady state, given by a droplet hanging from thebottom of the cylinder that meets the dry region withzero contact angle. The droplet minimizes the energy andattracts all strong solutions that satisfy certain energyand entropy inequalities. (Such solutions exist for arbitraryinitial values of finite energy and entropy, but it is notknown if they are unique.) The distance of any solutionfrom the steady state decays no faster than a power law.

Nash Equilibria for a simple model of market with commodity money.

Series
Math Physics Seminar
Time
Wednesday, February 16, 2011 - 16:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Federico BonettoGeorgia Tech
I'll present a simple model of market where the use of (commodity) money naturally arisefrom the agents interaction. I'll introduce the relevant notion of (Nash) equilibrium and discuss itsexistence and properties.

The commutator approach to semiclassical inequalities

Series
Math Physics Seminar
Time
Wednesday, February 9, 2011 - 16:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Evans HarrellSoM Georgia Tech
I'll describe some connections between identities for commutators and boundson eigenvalues, including Stubbe's proof of classical Lieb-Thirringinequalities and other sharp Lieb-Thirring inequalities for different models(including Schrödinger operators with periodic potentials or on manifolds,and quantum graphs).

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 LossGeorgia 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.

About symmetry and symmetry breaking for extremal functions in interpolation functional inequalities

Series
Math Physics Seminar
Time
Wednesday, January 19, 2011 - 16:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Maria J. EstebanCEREMADE, University of Paris, Dauphine
In this talk I will present recent work, in collaboration with J.Dolbeault, G. Tarantello and A. Tertikas,about the symmetry properties of extremal functions for (interpolation)functional inequalities playing an important rolein the study of long time behavior of evolution diffusion equations.Optimal constants are rarely known,in fact one can write them explicitely only when the extremals enjoymaximal symmetry. This is why the knowledge of the parameters' regionswhere symmetry is achieved is of big importance. In the case of symmetrybreaking, the underlying phenomena permitting it are analyzed.

Cohomological equations on dynamical systems arising from Delone sets.

Series
Math Physics Seminar
Time
Thursday, April 15, 2010 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Dr Alvaro Daniel CoronelFacultad de Matematicas, Pontificia Universidad Catolica de Chile, Santiago, Chile

Please Note: The speaker is visiting Georgia Tech for the full week. His office will be Skiles 133A.

This talk concerns aperiodic repetitive Delone sets and the dynamical systems associated with them. A typical example of an aperiodic repetitive Delone set is given by the set of vertices of the Penrose tiling. We show that natural questions concerning aperiodic repetitive Delone sets are reduced to the study of some cohomological equations on the associated dynamical systems. Using the formalism of tower systems introduced by Bellissard, Benedetti, and Gambaudo, we will study the problem about the existence of solution of these cohomological equations.

The McKean--Vlasov Equation in Finite Volume

Series
Math Physics Seminar
Time
Thursday, September 3, 2009 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Lincoln ChayesUCLA
The McK--V system is a non--linear diffusion equation with a non--local non--linearity provided by convolution. Recently popular in a variety of applications, it enjoys an ancient heritage as a basis for understanding equilibrium and near equilibrium fluids. The model is discussed in finite volume where, on the basis of the physical considerations, the correct scaling (for the model itself) is identified. For dimension two and above and in large volume, the phase structure of the model is completely elucidated in (somewhat disturbing) contrast to dynamical results. This seminar represents joint work with V. Panferov.

Dilute Quantum Gases

Series
Math Physics Seminar
Time
Monday, January 12, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Robert SeiringerPrinceton University
We present an overview of mathematical results on the low temperature properties of dilute quantum gases, which have been obtained in the past few years. The discussion includes, for instance, results on the free energy in the thermodynamic limit, and on Bose-Einstein condensation, Superfluidity and quantized vortices in trapped gases. All these properties are intensely being studied in current experiments on cold atomic gases. We will give a brief description of the mathematics involved in understanding these phenomena, starting from the underlying many-body Schroedinger equation.

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