Integrable Models in Statistical Mechanics, Limit Shapes and Combinatorics

Scientific goals and directions

In the last two decades, a remarkable development took place at the interface of combinatorics, probability theory and statistical mechanics. It resulted in a new development in several well-established topics. In particular, probabilistic aspects of solvable models in statistical mechanics such as the structure of Gibbs measure in the thermodynamical limit and the structure of large deviations are much better understood now.

The following topics, will lie at the core of the Summer School and the Conference:

--The structure Gibbs measures in the thermodynamic limit and the limit shape phenomenon;
--Enumerative combinatorics and integrability;
--Discrete geometry, discrete holomorphycity and conformal invariance in statistical mechanics,
--Mathematically rigorous foundation of the Kardar-Parisi-Zhang scaling and the theory of random matrices;
--Connection between integrable systems, statistical mechanics, the geometry of moduli spaces and representation theory.

Lecturers at the school (5 lectures, 4 hours lectures each):

Financial support

The school and research conference are organised by EIMI and supported by the Simons Foundation .

The organizers will be able to cover travel expenses and to provide accommodation for a limited number of participants, both of the Summer School and the Conference.