[Liste-CICMA] SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY (05/05/2016, J.Weinstein, K.Ford, Y. Martin)

Guillermo Martinez-Zalce martinez at crm.umontreal.ca
Tue May 3 09:52:30 EDT 2016


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SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY

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DATE :
Le jeudi 5 mai 2016 / Thursday, May 5, 2016

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

CONFERENCIER(S) / SPEAKER(S) :
Jared Weinstein (Boston University)

TITRE / TITLE :
The Lefschetz trace formula for rigid spaces, and the Kottwitz conjecture

LIEU / PLACE :
McGill University, Burnside Hall salle BH920

RESUME / ABSTRACT :
We report on work in progress with Tasho Kaletha.  The Lefschetz trace formula can be used to calculate the cohomology of many sorts of objects (manifolds, schemes, rigid spaces...), by counting the number of fixed points of an endomorphism.  But if the object is not compact, one can only apply the formula if the endomorphism has "no fixed points at infinity".  In this work we focus on certain rigid spaces called Rapoport-Zink spaces, which are important to the local Langlands program.  Following Mieda's work on the Lubin-Tate tower, we show that, so long as the "no fixed points at infinity" condition is satisfied, these spaces behave in ways predicted by the Kottwitz conjecture. 


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DATE :
Le jeudi 5 mai 2016 / Thursday, May 5, 2016

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

CONFERENCIER(S) / SPEAKER(S) :
Kevin Ford (UIUC)

TITRE / TITLE :
Large gaps between consecutive prime numbers and related problems

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

RESUME / ABSTRACT :
We describe recent advances on the problem of large gaps between consecutive prime numbers, in joint work with Ben Green, Sergei Konyagin, James Maynard and Terence Tao.  We will describe some related problems and applications, including chains of  large prime gaps, long strings of composites containing a perfect k-th power, and application to the least prime in an arithmetic progression.

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DATE :
Le jeudi 5 mai 2016 / Thursday, May 5, 2016

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

CONFERENCIER(S) / SPEAKER(S) :
Yves Martin (Chile)

TITRE / TITLE :
On the integral kernel for a multiple Dirichlet series associated to Siegel cusp forms

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

RESUME / ABSTRACT :
Let F be any weight k Siegel cusp form over the symplectic group Sp(2, \Z). The Koecher-Maass series D(F, w) is a single variable Dirichlet series constructed with the Fourier coefficients of F. If U is a Maass waveform, one can define the twisted Koecher-Maass series D(F, U, w). In particular, if we let U runs over all waveforms with eigenvalue in the continuum spectrum then the collection of such twisted Koecher-Maass series is a two variables Dirichlet series D(F, s, w). In this talk I introduce a
kernel which gives an integral representation of D(F, s, w) for all F. Then I discuss about a) the main analytic properties of D(F, s, w) that one gets from those of the kernel, b) how to write D(F, s, w) as an infinite sum of Dirichlet series associated to the Jacobi forms in the Fourier-Jacobi expansion of F, and c) a set of Fourier coefficients indexed by  diagonal matrices which characterize Siegel cusp forms of degree two.


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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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