**Title: Microscopic description of Coulomb-type systems
**

**Abstract:**

We are interested in systems of points with Coulomb, logarithmic or more

generally Riesz interactions (i.e. inverse powers of the distance). They

arise in various settings: an instance is the classical Coulomb gas which

in some cases happens to be a random matrix ensemble, another is vortices

in the Ginzburg-Landau model of superconductivity, where one observes in

certain regimes the emergence of densely packed point vortices forming

perfect triangular lattice patterns named Abrikosov lattices, a third is

the study of Fekete points which arise in approximation theory.

After reviewing the motivations, we will take a point of view based on the

detailed expansion of the interaction energy to describe the microscopic

behavior of the systems. In particular a Central Limit Theorem for

fluctuations and a Large Deviations Principle for the microscopic point

processes are given.

This allows to observe the effect ofÂ the temperature as it gets very

large or very small, and to connect with crystallization questions.

The main results are joint with Thomas Lebl\’e and also based on previous

works with Etienne Sandier, Nicolas Rougerie and Mircea Petrache.

Wednesday, October 26, 4:30 – 5:30 p.m.

Mathematics 520

Tea will be served at 4:00 p.m.