On the heat kernel of a Cayley graph of PSL_2Z (Kamila Kashaeva, UNIGE)

04.11.2025 10:30

The heat kernel of a graph encodes information about its geometry and the Laplace spectrum. Following the work of Fan Chung and Shing-Tung Yau, I will talk about coverings of weighted graphs and explain how they can be used to relate the corresponding heat kernels. I will then describe an application of this method to a specific Cayley graph of the modular group PSL_2Z. This leads to an explicit formula for its heat kernel and allows one to determine the Laplace spectrum, which turns out to consist of two eigenvalues and two intervals.
Inspired by Selberg’s 1/4-conjecture, I will also formulate a conjecture about a lower bound for the spectral gap of Cayley graphs of PSL_2F_p with the same generators as for PSL_2Z.
This is a joint work with Anders Karlsson.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Séminaire "Groupes et géométrie"

entrée libre