Introduction to Expander and Ramanujan Graphs

• Event: Student Talks (Fall 2025)
• Organiser: Math Club, ISI Bengaluru Centre
• Venue: Second Floor Auditorium, Academic Building, ISI Bengaluru
• Date: 20 October, 2025
• Abstract: How can a network be both sparse, with few connections, and yet highly connected? This talk is about expander graphs, which are structures that manage this trade-off surprisingly well. Indeed, this structural property is the source of their utility across diverse areas of theoretical computer science and pure mathematics, forming a bridge between combinatorics, group theory, and number theory. We will proceed by defining these graphs rigorously and surveying their key properties and applications, assuming minimal knowledge of graph theory and eigenvalues.