[Liste-CICMA] SÉM. QUÉBEC-VERMONT NUMBER THEORY (17/04/2014, X. Wan, L. Candelori, K. Henriot, C. Gomez)

Dimitris Koukoulopoulos koukoulo at DMS.UMontreal.CA
Wed Apr 16 17:07:55 EDT 2014


Second announcement, with revised titles and abstracts:


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SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY

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DATE :
Le jeudi 17 avril 2014 / Thursday, April 17, 2014

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

CONFERENCIER(S) / SPEAKER(S) :
Xin Wan (IAS)

TITRE / TITLE :
TBA

LIEU / PLACE :
McGill University, Burnside Hall 920

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DATE :
Le jeudi 17 avril 2014 / Thursday, April 17, 2014

HEURE / TIME :
14 h - 16 h 00 / 2:00 p.m. - 4:00 p.m.

CONFERENCIER(S) / SPEAKER(S) :
Graduate student presentations (Luca Candelori, Kevin Henriot, Clement
Gomez)

TITRE / TITLE :
Luca Candelori. Metaplectic stacks and vector-valued modular forms.
ABSTRACT: Given a positive definite lattice L and an integer k, we give a
geometric interpretation of vector-valued modular forms of weight k/2
attached to L, in the sense of Borcherds. Our geometric interpretation is
inspired by that given by Katz in the case of classical integral weight
modular forms. In particular, we construct vector bundles over the moduli
stack of elliptic curves whose sections over the complex numbers correspond
to vector-valued modular forms. Our constructions makes use of auxiliary
'metaplectic stacks', which are gerbes over the modular stack. All
constructions take place over the integers, and can be used to give, for
example, a notion of vector-valued modular forms mod p. Kevin Henriot.
Linear structures of low complexity in the primes Abstract: The celebrated
Green-Tao theorem asserts the existence of arbitrarily long arithmetic
progressions in every subset of the prime of positive upper density, and it
extends to all translation-invariant linear patterns of finite complexity.
On the other hand, a quantitative result of Helfgott and de Roton says that
a subset of the primes up to N of density (log log N)^{ - 1/3 } contains a
three-term arithmetic progression. In this talk we discuss an intermediate
result, which finds quantitative bounds of the shape (log log N)^-c for
linear patterns of complexity one. Clement Gomez. Euler systems and
Kolyvagin systems.



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




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Responsable(s) :
Henri Darmon (darmon at math.mcgill.ca)
Andrew Granville (andrew at dms.umontreal.ca)
Dimitris Koukoulopoulos (koukoulo at CRM.UMontreal.CA)
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*http://www.dms.umontreal.ca/~qvnts/QVNTSinfo.html
<http://www.dms.umontreal.ca/~qvnts/QVNTSinfo.html>*
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