Geometry and Topology Seminar: "Automorphic functions via noncommutative geometry"

Abstract: In this talk we discuss noncommutative spaces arising naturally in number theory. Considering elliptic curves together with their torsion structure leads to the notion of Q-lattice introduced by Connes and Marcolli. The relation of commensurability among Q-lattices gives rise to a quantum statistical mechanical system with a rich structure encoding the arithmetic of automorphic functions. Looking at automorphic functions from the vantage point of noncommutative geometry provides new tools and insights for their study. We will discuss the Connes-Marcolli system in relation to the "big picture", a combinatorial gadget introduced by Conway for the study of congruence groups. We will also explore the relevance of this setting for the study of principal moduli.

Host: Michael Landry