[Liste-CICMA] SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY (21/04/2016, George Pappas, Adriana Salerno, Adam Logan)

Guillermo Martinez-Zalce martinez at CRM.UMontreal.CA
Wed Apr 20 09:28:28 EDT 2016


TITLE OF ADAM LOGAN’S TALK ADDED..

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SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY

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DATE :
Le jeudi 21 avril 2016 / Thursday, April 21, 2016

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

CONFERENCIER(S) / SPEAKER(S) :
George Pappas (Michigan State University)

TITRE / TITLE :
On some Rapoport-Zink formal scheme

LIEU / PLACE :
McGill University, Burnside Hall salle BH920

RESUME / ABSTRACT :
We will describe constructions of certain Rapoport-Zink type formal schemes that uniformize the completions of Hodge type Shimura varieties along certain loci of their fibers modulo primes. We will explain two different approaches to constructing these, one given in joint work with B. Howard and the other in joint work with O. Bueltel.

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DATE :
Le jeudi 21 avril 2016 / Thursday, April 21, 2016

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

CONFERENCIER(S) / SPEAKER(S) :
Adriana Salerno (Bates College)

TITRE / TITLE :
Arithmetic Mirror Symmetry of K3 Surfaces and Hypergeometric Functions.

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

RESUME / ABSTRACT :
Mirror symmetry predicts surprising geometric correspondences between distinct families of algebraic varieties.  In some cases, these correspondences have arithmetic consequences. Among the arithmetic correspondences predicted by mirror symmetry are correspondences between point counts over finite fields. In particular, we explore closed formulas for the point counts for our alternate mirror families of K3 surfaces, their relation to their Picard-Fuchs equations and hypergeometric functions. This is joint work with: Charles Doran (University of Alberta, Canada), Tyler Kelly (University of Cambridge, UK), Steven Sperber (University of Minnesota, USA), John Voight (Dartmouth College, USA), and Ursula Whitcher (University of Wisconsin, Eau Claire, USA).

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DATE :
Le jeudi 21 avril 2016 / Thursday, April 21, 2016

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

CONFERENCIER(S) / SPEAKER(S) :
Adam Logan (Government of Canada)

TITRE / TITLE : Modularity of some Calabi-Yau threefolds coming from physics

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

RESUME / ABSTRACT :
The correspondence between elliptic curves over $\mathbb Q$ up to isogeny and modular forms of weight $2$ (due in one direction to Eichler and Shimura, in the other mostly to Wiles) is at the heart of modern arithmetic geometry.  One would like to generalize to modular forms of weight greater than $2$.  Brown and Schnetz, motivated by ideas from physics, constructed certain varieties and observed that their numbers of points mod $p$ sometimes matched the coefficients of modular forms.  In this talk I will explain how I proved this in one of their examples in which no variety corresponding to the modular form was previously known.  Time permitting, I will also describe how I have found varieties matching other modular forms by exploring nearby regions of an appropriate moduli space.


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Responsable(s) :
Henri Darmon (darmon at math.mcgill.ca <mailto:darmon at math.mcgill.ca>)
Andrew Granville (andrew at dms.umontreal.ca <mailto:andrew at dms.umontreal.ca>)
Dimitris Koukoulopoulos (koukoulo at dms.umontreal.ca <mailto:koukoulo at dms.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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