[Liste-CICMA] SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY (25/02/2016, Christelle Vincent, Aryan Farzad)

Guillermo Martinez-Zalce martinez at crm.umontreal.ca
Tue Feb 23 10:12:10 EST 2016


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SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY

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DATE :
Le jeudi 25 février 2016 / Thursday, February 25, 2016

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

CONFERENCIER(S) / SPEAKER(S) :
Christelle Vincent (University of Vermont)

TITRE / TITLE :
Computing equations of hyperelliptic curves whose Jacobian has CM


LIEU / PLACE :
McGill University, Burnside Hall salle BH920

RESUME / ABSTRACT :
It is known that given a CM sextic field, there exists a non-empty finite set of abelian varieties of dimension 3 that have complex multiplication by this field. Under certain conditions on the field and the CM-type, this abelian variety can be guaranteed to be principally polarizable and simple. This ensures that the abelian variety is the Jacobian of a hyperelliptic curve or a plane quartic curve.

In this talk, we begin by showing how to generate a full set of period matrices for each isomorphism class of simple, principally polarized abelian variety with CM by a sextic field K. We then show how to determine whether the abelian variety is a hyperelliptic or plane quartic curve. Finally, in the hyperelliptic case, we show how to compute a model for the curve.

This is joint work with J. Balakrishnan, S. Ionica and K. Lauter.


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DATE :
Le jeudi 25 février 2016 / Thursday, February 25, 2016

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

CONFERENCIER(S) / SPEAKER(S) :
Aryan Farzad (Centre de recherches mathématiques)

TITRE / TITLE :
Distribution of Squares Modulo a Composite Number

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

RESUME / ABSTRACT :
For q square-free, we call an integer s a square modulo q if and only if s is a square modulo p for all primes p dividing q. In this talk we look the variance of the distribution of squares modulo a composite number. We also look at inverse questions for the large sieve in distribution aspect and  make some improvements regarding distribution of tuples of reduced residues. 


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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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