[Liste-CICMA] SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY (05/11/2015, Cameron Franc, Nicolas Templier)

Guillermo Martinez-Zalce martinez at crm.umontreal.ca
Wed Nov 4 10:06:07 EST 2015


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SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY

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DATE :
Le jeudi 5 novembre 2015 / Thursday, November 5, 2015

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

CONFERENCIER(S) / SPEAKER(S) :
Cameron Franc (Michigan and Santa Cruz)

TITRE / TITLE :
On the structure of modules of vector valued modular forms

LIEU / PLACE :
McGill University, Burnside Hall salle BH920

RESUME / ABSTRACT :
Associated with a finite dimensional complex representation of SL_2(Z) is a collection of vector valued modular forms. The corresponding module of vector valued modular forms for a fixed representation is known to be free of finite rank (equal to the dimension of the representation) over the ring of classical scalar forms of level one. This free-module theorem was first proved by Marks-Mason. We will explain, using joint work with Luca Candelori, how the free-module theorem follows from the splitting principle for vector bundles on the moduli stack of elliptic curves. An important related problem is to determine the structure of this free-module. In particular, one would like to know the weights of a generating set of vector valued forms. In the second part of our talk we will discuss recent joint work with Geoff Mason that establishes certain bounds on these weights, and bounds on the multiplicities of the generating weights.


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DATE :
Le jeudi 5 novembre 2015 / Thursday, November 5, 2015

HEURE / TIME :
14 h - 15 h 30 / 2:00 p.m. - 3:30 p.m.

CONFERENCIER(S) / SPEAKER(S) :
Nicolas Templier (Cornell)

TITRE / TITLE :
Weyl’s law in the theory of automorphic forms

LIEU / PLACE :
Concordia University, Library Building, 9th floor

RESUME / ABSTRACT :
The automorphic spectrum contains the Laplace and Hecke eigenvalues attached to automorphic forms on locally symmetric spaces. The Weyl's law consists in counting Maass forms in a spectral window, and more generally counting automorphic representations with prescribed local behavior at certain places. Known results for SL(2) follow from applying the Selberg trace formula. In works with S.W.Shin, P.Sarnak, J.Matz and J.-L.Kim we have generalized some of the classical results to higher rank groups. Consequences are a refinement of the Katz-Sarnak heuristics and bounds on average towards the Ramanujan conjecture which are are unconditional on SL(n,R)/SO(n).


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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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http://www.dms.umontreal.ca/~qvnts/QVNTSinfo.html


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