In this talk I will consider finite graphs whose vertexes are supersingular elliptic curves, possibly with level structure, and edges are isogenies. They can be applied to the study of modular forms and to isogeny based cryptography. The main result I will present is an upper bound on the modules of the eigenvalues of their adjacency matrices, which in particular implies that these graphs are Ramanujan. I will also discuss the asymptotic distribution of the eigenvalues of the adjacency matrices, the number of connected components, the automorphisms of the graphs, and the connection between the graphs and modular forms. This is based on a joint work with Guido Lido.
Spectral theory of isogeny graphs
04.03.2025 13:15 - 14:45
Organiser:
H. Grobner, A. Minguez-Espallargas, A. Mellit
Location: