An analogue of a conjecture of Hausel-Rodriguez-Villegas for number fields
Date:
Wednesday, April 19, 2017 13:45 - 15:45
Speaker:
Pierre-Henri Chaudouard (Université Paris 7)
Location:
Seminar room Big Ground floor / Office Bldg West (I21.EG.101)
Series:
Mathematics and CS Seminar
Host:
Tamas Hausel
Contact:
DE ANTONI Jessica
The Arthur-Selberg trace formula is a central tool in the field of automorphic forms. An open question is to understand or compute its unipotent contribution. For function fields, this question is among others related to the counting of Higgs bundles which has a conjectural expression (Hausel-Rodriguez-Villegas-Mozgovoy). In this talk, in the case of number fields:
-- we will give a (refined) conjectural expression à la Hausel-Rodriguez-Villegas for the unipotent part of the Arthur-Selberg trace formula for a "basic test function".
-- inspired by a work of Schiffmann on Higgs bundles, we will give an expression for this unipotent contribution for a large class of test functions.