# [Liste-CICMA] SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY (06/10/2016, Luca Candelori, Bruno Martin, Andrea Conti)

Guillermo Martinez-Zalce martinez at crm.umontreal.ca
Mon Oct 3 12:01:13 EDT 2016

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SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY

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DATE :
Le jeudi 6 octobre 2016 / Thursday, October 6, 2016

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

CONFERENCIER(S) / SPEAKER(S) :
Luca Candelori (LSU)

TITRE / TITLE :
The transformation laws of algebraic theta functions

LIEU / PLACE :
McGill University, Burnside Hall salle BH920

RESUME / ABSTRACT :
We present the algebro-geometric theory underlying the classical transformation laws of theta functions with respect to the action of symplectic matrices on Siegel's upper half-space. More precisely, we explain how the theta multiplier, the half-integral weight automorphy factor and the Weil representation occurring in the classical transformation laws all have a geometric origin, that is, they can all be constructed within a given moduli problem on abelian schemes. To do so, we introduce and study new algebro-geometric constructions such as theta multiplier bundles, metaplectic stacks and
bundles of half-forms, which could be of independent interest. Applications include a geometric theory of modular forms of half-integral (in the sense of Shimura), and their generalizations to higher degree, as well as giving new, explicit formulas for
determinant bundles on abelian schemes.

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DATE :
Le jeudi 6 octobre 2016 / Thursday, October 6, 2016

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

CONFERENCIER(S) / SPEAKER(S) :
Bruno Martin (Université du Littoral)

TITRE / TITLE :
On prime numbers with as many ones as zeros in their binary expansion

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

RESUME / ABSTRACT :
Drmota, Mauduit and Rivat showed in 2009 that the set $E$ of prime numbers with as many ones as zeros in their binary expansion is infinite (they actually gave an asymptotic formula for $\sharp E \cap [1,N]$ for $N>2$). We prove that for every irrational number $\beta$, the sequence $(\beta p)_{p\in E}$ is uniformly distributed modulo 1. This is a joint work with Christian Mauduit and Joël Rivat (Université d’Aix-Marseille).

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DATE :
Le jeudi 6 octobre 2016 / Thursday, October 6, 2016

HEURE / TIME :
16 h - 17 h / 4:00 p.m. - 5:00 p.m.

CONFERENCIER(S) / SPEAKER(S) :
Andrea Conti (CICMA)

TITRE / TITLE :
Big Galois image for p-adic families of finite slope modular forms

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

RESUME / ABSTRACT :
I present the result of a joint work with A. Iovita and J. Tilouine. We study the image of the Galois representation associated with a p-adic family of modular forms of finite positive slope. We prove that this image is big, in a precise sense, and that its size can be described in terms of the congruences of the family with overconvergent CM eigenforms. These results are analogous to those obtained by H. Hida and J. Lang for ordinary families.

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Responsable(s) :
Henri Darmon (darmon at math.mcgill.ca)
Eyal Z. Goren (eyal.goren at mcgill.ca)
Chantal David (cdavid at mathstat.concordia.ca)
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http://www.dms.umontreal.ca/~qvnts/QVNTSinfo.html