An introduction to expander families

• Grant number: 15/24591-3
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: February 01, 2016
• End date: January 31, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Igor Mencattini
• Grantee: Daniela Arantes Gomes Ferreira
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

We aim to study an elementary proof that the so called Ramanujan graphs form a family of expander graphs. To this end, after introducing the elementary notions from algebra and graph theory we will first introduce the concept of Cayley graph, then we consider the Ramanujan graphs and we will prove that they form an expander family.