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Integrable systems and partition functions of random matrix models

Grant number: 20/02746-3
Support type:Scholarships in Brazil - Master
Effective date (Start): April 01, 2020
Effective date (End): February 28, 2022
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal Investigator:Guilherme Lima Ferreira da Silva
Grantee:Carla Mariana da Silva Pinheiro
Home Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Associated research grant:19/16062-1 - Asymptotic analysis of interacting particle systems and random matrix theory, AP.JP

Abstract

One of the central objects in Statistical Mechanics is the partition function of a given model, from which one can infer phase transitions and compute a diversity of different statistics on the model. As such, the partition function also plays a central role in the theory of random matrices. On an apparent distinct world, integrable systems are a very distinguished class of differential systems that admit exact solutions and beautiful symmetries. But these two worlds started to come together in the late 90's, when it was found out that the partition function of different random matrix models are actually solutions to important classes of integrable systems. The main goal of this M.D. Proposal is to understand some of these connections, and explore how they can be used for a better understanding of random matrix models. (AU)