[Liste-CICMA] SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY (09/02/2017, Evan Dummit, Jan Vonk)

Guillermo Martinez-Zalce martinez at crm.umontreal.ca
Mon Feb 6 14:25:04 EST 2017


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SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY

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DATE :
Le jeudi 9 février 2017 / Thursday, February 9, 2017

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

CONFERENCIER(S) / SPEAKER(S) :
Evan Dummit (Rochester)

TITRE / TITLE :
Counting Number Fields by Discriminant

LIEU / PLACE :
McGill University, Burnside Hall salle BH920

RESUME / ABSTRACT :
The problem of analyzing the number of number field extensions $L/K$ with bounded (relative) discriminant has been the subject of renewed interest in recent years, with significant advances made by Ellenberg-Venkatesh, Bhargava-Shankar, and numerous others.  I will give an overview of the history of this problem and what results are known (or conjectured), and then discuss a series of results, involving similar techniques to those of Ellenberg-Venkatesh, for upper bounds on the number of extensions $L/K$ where the Galois group of the Galois closure is also specified.  Time permitting, I will also discuss some related counting questions involving variants on the classical discriminant.


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DATE :
Le jeudi 9 février 2017 / Thursday, February 9, 2017

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

CONFERENCIER(S) / SPEAKER(S) :
Jan Vonk (CICMA)

TITRE / TITLE :
Towers of modular curves

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

RESUME / ABSTRACT :
During a failed attempt to find explicit generators of class fields of real quadratic number fields, we are led to consider two spaces of modular forms that have a mysterious aura around them: Modular forms "at the boundary of weight space" and modular forms whose eigenvalue of U_p is zero. We present new results in both settings, and make these spaces amenable to concrete experimentation. 


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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


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