Isogenic Graphs: Spectral Analysis and Mathematical Applications

This lecture delves into the study of isogenic graphs, focusing on their spectral properties and mathematical applications. The instructor presents results obtained through joint work, using modular forms to prove theorems related to these graphs. The discussion covers the concept of isogenic graphs with level structures, highlighting the importance of Borel level structures. The lecture explores the spectral graph theory, emphasizing the connection between the spectrum of a graph and its properties. Additionally, the instructor explains the significance of the spectral gap in determining the connectedness of a graph and its mixing time in mathematical physics and cryptography.