BC-MIT Number Theory Seminar

Tuesday, December 03, 2019 at 3:00pm to 4:00pm


SPEAKER:  Bao Le Hung (Northwestern University)

TITLE:  "Serre Weights, Breuil-Mezard Cycles and Deformed Affine Springer Fibers"

ABSTRACT:  Given a locally symmetric space and a mod p system of Hecke eigenvalues, the weight part of Serre's conjecture seeks to classify the cohomology groups of the locally symmetric space where this system of eigenvalues contribute. Via Taylor-Wiles patching, this problem is known to be closely linked to the Breuil-Mezard conjecture, which predicts a representation-theoretic recipe to build mod p fibers of local Galois deformation rings (and more generally, the Emerton-Gee moduli stack of local Galois representation) out of atomic pieces corresponding to Serre weights. I will describe progress on both questions in many cases, via a theory of local models, which relates (portions of) the Emerton-Gee stack to mixed characteristics versions of (deformed) affine Springer fibers.

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Department of Mathematics

##MIT, #Number Theory Seminar, #Bjorn Poonen, #Bao Le Hung, #Northwester University

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