Cursos a desarrollar
Sistemas discretos integrables
Matteo Mucciconi
National University of Singapore
Abstract:
Integrable systems are dynamical systems possessing a large number of conservation laws. As such they possess interesting physical properties which can be analyzed with rigorous mathematical methods.
In these lectures we will first consider the box and ball system (BBS) as a prototypical example of an integrable system in discrete time and space. After reviewing basic results on the BBS we will consider the model started with random initial conditions and ask probabilistic questions such as construction and characterization of invariant measures.
I will then move to a higher dimensional generalization of the BBS, introduced by Sasamoto, Imamura and myself and show that, analysing the model with certain random initial conditions one can produce highly nontrivial relations between different probability measures on partitions.
Particiones Aleatorias
César Cuenca
The Ohio State University
Abstract:
Lecture 1: Why random partitions?
In this introductory lecture, I will explain the connection between random partitions and models from statistical mechanics (lozenge tilings) and representation theory. I will also briefly discuss the parallelism between random partitions and random matrices.
Lecture 2: Lozenge tilings and Schur polynomials.
In the second lecture, I will introduce the symmetric Schur polynomials, derive some basic properties, connect them to the model of uniformly random lozenge tilings and start studying the behavior of random lozenge tilings in the tangent region.
Lecture 3: Random matrix theory.
In this last lecture, we continue the study of lozenge tilings in the tangent region. I will finish with a brief discussion of problems of current research interest in random matrix theory.
