Quantum Statistical Mechanics, L-series, and Anabelian Geometry

Speaker: Prof.  Matilde Marcolli (California Institute of Technology)

Time: 2013-08-06, 3:00pm

Venue: Conference Hall 213, Science Building, Tsinghua University

Abstract: The talk is based on joint work with Gunther Cornelissen. I will show how quantum statistical mechanical systems associated to number field provide complete invariants that permit the reconstruction of the number field up to isomorphism, even though some of their main constituent elements by themselves (the abelianized Galois group, the Dedekind zeta function, and the ring of adeles) are not complete invariants. In particular, using these quantum statistical mechanical methods, we obtained a new purely number theoretic result, showing that a number field can be reconstructed from the associated family of L-functions with Grossencharacter.