# [Liste-CICMA] SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY (03/11/2016, S. Dasgupta, L. Garcia, E. De Salit)

Guillermo Martinez-Zalce martinez at crm.umontreal.ca
Tue Nov 1 09:41:41 EDT 2016

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SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY

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DATE :
Le jeudi 3 novembre 2016 / Thursday, November 3, 2016

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

CONFERENCIER(S) / SPEAKER(S) :
Samit Dasgupta (UCSC)

TITRE / TITLE :
On the Gross--Stark Conjecture

LIEU / PLACE :
McGill University, Burnside Hall salle BH920

RESUME / ABSTRACT :
In 1980, Gross conjectured a formula for the expected leading term at s=0 of the Deligne--Ribet p-adic L-function associated to a totally even character $\psi$ of a totally real field F. The conjecture states that after scaling by $L(\psi \omega^{-1}, 0)$, this value is equal to a p-adic regulator of units in the abelian extension of F cut out by $\psi\omega^{-1}$. In this talk we describe a proof of Gross's conjecture. This is joint work with Mahesh Kakde and Kevin Ventullo.

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DATE :
Le jeudi 3 novembre 2016 / Thursday, November 3, 2016

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

CONFERENCIER(S) / SPEAKER(S) :
Luis Garcia (Toronto)

TITRE / TITLE :
Superconnections and special cycles

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

RESUME / ABSTRACT :
I will start by explaining Quillen's notion of a superconnection, and then will use it to define some natural differential forms on period domains parametrizing Hodge structures. For hermitian symmetric domains, we will show that this construction recovers the forms introduced by Kudla and Millson. We will discuss the properties of these forms and how they allow to generalize results on special cycles in Shimura varieties to arithmetic quotients of period domains.

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DATE :
Le jeudi 3 novembre 2016 / Thursday, November 3, 2016

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

CONFERENCIER(S) / SPEAKER(S) :
E. De Shalit (Hebrew University)

TITRE / TITLE :
\mu-ordinary foliations on Picard modular surfaces

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

RESUME / ABSTRACT :
The first half of the talk will be a survey of old results of Jacobson and Rudakov-Shafarevich classifying inseparable morphisms between smooth varieties by means of certain foliations in the tangent bundle. In the second half we shall apply this notion to Picard modular surfaces to obtain some new results. We will end the talk with speculations on higher dimensional Shimura varieties, and a conjecture in the Andre-Oort style. This is joint work with Eyal Goren.

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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