[Liste-CICMA] SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY (22/03/2018, Marc-Hubert Nicole, Alexandra Florea)

Guillermo Martinez-Zalce martinez at crm.umontreal.ca
Tue Mar 20 09:37:28 EDT 2018


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SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY

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DATE :
Le jeudi 22 mars 2018 / Thursday, March 22, 2018

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

CONFERENCIER(S) / SPEAKER(S) :
Marc-Hubert Nicole (Université Marseille)

TITRE / TITLE :
Drinfeld Modular Varieties for GL(N) and Families of Modular Forms

LIEU / PLACE :
McGill University, Burnside Hall salle BH920

RESUME / ABSTRACT :
Classical modular curves associated to GL(2) are moduli spaces of elliptic curves with additional structure. Taking advantage of the analogy between number fields and function fields, Drinfeld modules (of rank 2) were introduced as a good analogue of elliptic curves. While there are no Shimura varieties associated to the general linear group GL(N) for N>2, the situation is sharply different over function fields. The Drinfeld modular variety for GL(N) is the moduli space of Drinfeld modules of rank N (with level structure). It is an affine scheme of dimension N-1. In this talk, I will explain how various analogues of well-established theories in the classical context extend to Drinfeld modular varieties and their modular forms: the canonical subgroup, generalized Hasse invariants, Katz’s theory of p-adic modular forms and Hida's theory of families of modular forms. 

Some of the results were obtained in joint work with F. Trihan (Tôkyô) and some others with G. Rosso (Montréal).

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DATE :
Le jeudi 22 mars 2018 / Thursday, March 22, 2018

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

CONFERENCIER(S) / SPEAKER(S) :
Alexandra Florea (Bristol University)

TITRE / TITLE :
Moments of cubic L-functions over function fields

LIEU / PLACE :
Concordia University, Library Building, 9th floor, room LB 921-4

RESUME / ABSTRACT :
I will talk about some recent work with Chantal David and Matilde Lalin about the mean value of L-functions associated to cubic characters over F_q[t] when q=1 (mod 3). I will explain how to obtain an asymptotic formula with a (maybe a little surprising) main term, which relies on using results from the theory of metaplectic Eisenstein series about cancellation in averages of cubic Gauss sums over functions fields.

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Responsable(s) :
Henri Darmon (Henri.darmon at mcgill.ca)
Adrian Iovita (adrian.iovita at concordia.ca)
Maksym Radziwill (maksym.radziwill at gmail.com)
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