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Series: Math Physics Seminar

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.

Series: Math Physics Seminar

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).

Series: Math Physics Seminar

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

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.

Series: Math Physics Seminar

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.

Series: Math Physics Seminar

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.

Series: Math Physics Seminar

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.