Integrable systems and partition functions of random matrix models

• Grant number: 20/02746-3
• Support Opportunities: Scholarships in Brazil - Master
• Start date: April 01, 2020
• End date: 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
• Host 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)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

PINHEIRO, Carla Mariana da Silva. Integrable Systems and Partition Functions of Random Matrix Models. 2022. Master's Dissertation - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.