K-theory, Representation Theory and Automorphic Forms

11-12 September 2017, Sheffield

Organized by Paul Mitchener, Roger Plymen and Haluk Sengun

Automorphic forms are central objects in modern number theory with fascinating connections to many other parts of mathematics. The cohomological interpretation of modular forms, going back to works of Eichler and Shimura in the 1950's, is a key approach to automorphic forms that relates the cohomology of arithmetic manifolds to automorphic forms through representation theory of Lie groups. 

The recent paper [BS16] studies the K-theory/K-homology of certain C*-algebras ("arithmetic C*-algebras") that naturally arise from arithmetic manifolds. The results obtained in this paper raise the possibility of an approach to automorphic forms via the K-groups of arithmetic C*-algebras, akin to the well-known cohomological approach to automorphic forms. Our meeting will bring together a small group of experts in K-theory, representation theory and automorphic forms in order to develop these ideas.

Participants: 

Anne-Marie Aubert (Paris)

Tobias Berger (Sheffield)

Neil Dummigan (Sheffield)

Sergio Mendes (Lisbon)

Bram Mesland (Bonn) 

Paul Mitchener (Sheffield)

David O'Sullivan (Sheffield Hallam)

Roger Plymen (Southampton)

Haluk Sengun (Sheffield)

Christian Voigt (Glasgow)

Nick Wright (Southampton)

Joachim Zacharias (Glasgow)

Monday Programme

11:00 TALK 1 (Mitchener)

LUNCH

14:00 TALK 2 (Sengun)

15:30 TALK 3 (Mesland)

WORKSHOP DINNER

Tuesday Programme

10:00 TALK 4 (Wright)

11:30 TALK 5 (Aubert)

LUNCH

We gratefully acknowledge the support of

MSRC of the University of Sheffield

and