Abstract:

Ramanujan graphs, as a typical class of the so-called expander graphs, are important in graph theory, number theory as well as computer science. Expander complexes and Ramanujan complexes, as their higher dimensional analogues, have gradually attracted interest in the past decades. In this talk, we give a new construction of Ramanujan complexes from unitary groups over number fields, based on the endoscopic classification of (non-quasisplit) unitary groups. Under the "golden" condition, our construction is explicit, meaning that we have an algorithm that is practically executable on a modern (or future) computer. This is joint work with Rahul Dalal and Alberto Minguez.

Organizer: 李华杰