[Liste-CICMA] SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY (11/02/2016, Daniel Le, Michael Harris)

Guillermo Martinez-Zalce martinez at crm.umontreal.ca
Tue Feb 9 14:03:49 EST 2016


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SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY

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DATE :
Le jeudi 11 février 2016 / Thursday, February 11, 2016

HEURE / TIME :
10 h 30 - 12 h / 10:30 a.m. - 12:00 p.m.

CONFERENCIER(S) / SPEAKER(S) :
Daniel Le (University of Toronto)

TITRE / TITLE :
Potentially crystalline deformation rings and the cohomology of U(3) arithmetic manifolds

LIEU / PLACE :
McGill University, Burnside Hall salle BH920

RESUME / ABSTRACT :
We describe a method to calculate some potentially crystalline deformation rings for three dimensional Galois representations. We then discuss applications to the weight part of Serre's conjecture, mod p multiplicity one, and lattices in the cohomology of U(3) arithmetic
manifolds.


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DATE :
Le jeudi 11 février 2016 / Thursday, February 11, 2016

HEURE / TIME :
16 h - 15 h 30 / 4:00 p.m. - 3:30 p.m.

CONFERENCIER(S) / SPEAKER(S) :
Michael Harris (Columbia University)

TITRE / TITLE :
Modularity and potential modularity theorems in the function field setting.

LIEU / PLACE :
Concordia University, Library Building, 9th floor, Salle/Room 921-04

RESUME / ABSTRACT :
Let G be a reductive group over a global field of positive characteristic. In a major breakthrough, Vincent Lafforgue has recently shown how to assign a Langlands parameter to a cuspidal automorphic representation of G.
The parameter is a homomorphism of the global Galois group into the Langlands L-group $^LG$ of G. I will report on my joint work in progress with Böckle, Khare, and Thorne on the Taylor-Wiles-Kisin method in the setting of Lafforgue's correspondence.  New (representation-theoretic and Galois-theoretic) issues arise when we seek to extend the earlier work of Böckle and Khare on the case of GL(n) to general reductive groups.  I describe hypotheses on the Langlands parameter that allow us to apply modularity arguments unconditionally, and I will state a potential modularity theorem for a general split adjoint group.


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Responsable(s) :
Henri Darmon (darmon at math.mcgill.ca)
Andrew Granville (andrew at dms.umontreal.ca)
Dimitris Koukoulopoulos (koukoulo at dms.umontreal.ca)
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Séance de dédicaces / Book Signing Event
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http://www.crm.umontreal.ca/Harris


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