Introduction to combinatorial and geometric group theory

• Grant number: 16/11366-4
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: August 01, 2016
• End date: July 31, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Francesco Matucci
• Grantee: Bianca Boeira Dornelas
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

Combinatorial and Geometric Group Theory aim to connect algebraic properties of groups together with combinatorial, geometric and topological properties of spaces on which these groups act upon. In this project the student will study some fundamental tools of these two theories, such as groups acting on trees, diagram groups, amenable groups and automata groups. During the course of this study the student will learn tools such as graphs, 2-complexes, Van Kampen diagrams, growth in groups and some concepts from semigroup and language theory.