An introduction to ergodic theory with applications to number theory

• Grant number: 22/07208-5
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: September 01, 2022
• End date: December 31, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Ricardo Miranda Martins
• Grantee: André Boscariol Rasera
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 18/13481-0 - Geometry of control, dynamical and stochastic systems, AP.TEM

Abstract

In this project we will investigate the foundations of ergodic theory, with the aim of applying it to number theory problems. The two main theoretical results we will examine are the Poincaré Recurrence Theorem and the Ergodic Theorem. The methods and theorems studied will be applied to results on density of primes and to Weyls Theorem.(AU)