[Liste-CICMA] SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY (23/11/2017, Matteo Longo, Xiannan Li)
Guillermo Martinez-Zalce
martinez at crm.umontreal.ca
Mon Nov 20 11:25:14 EST 2017
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SÉMINAIRE QUÉBEC-VERMONT NUMBER THEORY
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DATE :
Le jeudi 23 novembre 2017 / Thursday, November 23, 2017
HEURE / TIME :
10 h 30 - 12 h / 10:30 a.m. - 12:00 p.m.
CONFERENCIER(S) / SPEAKER(S) :
Matteo Longo (University of Padova)
TITRE / TITLE :
On the p-adic variation of the Gross-Kohnen-Zagier theorem.
LIEU / PLACE :
McGill University, Burnside Hall salle BH920
RESUME / ABSTRACT :
Given an elliptic curve defined over the field of rational numbers and given an imaginary quadratic field K, one may define (using the theory of complex multiplication) a K-rational point of the elliptic curve, called Heegner point. Heegner points are crucial tools for studying the arithmetic of elliptic curves; in particular, the celebrated theorem of Gross and Zagier relates, under suitable arithmetic assumptions, the Neron-Tate height of Heegner points and the leading term of the complex L-function of E over K. The Gross-Kohnen-Zagier theorem (GKZ), complementary to the Gross-Zagier theorem mentioned above, shows that, under suitable arithmetic assumptions, the relative positions of the Heegner points, as the imaginary quadratic field varies while the elliptic curve stays fixed, are encoded by the Fourier coefficients of a Jacobi form. Briefly, Heegner points are generating series for Jacobi forms. Several generalizations of the GKZ theorem are available in the literature, by Kudla (putting things in a general perspective by the formulation of a series of conjectures, known as Kudla's program), Borcherds (using singular theta liftings) and Yuan-Zhang-Zhang (in the automorphic representation setting). In this seminar I will try to explore a further possible direction suggested by the GKZ theorem, where we make all objects vary in p-adic analytic families. This is a joint work with M.-H. Nicole.
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DATE :
Le jeudi 23 novembre 2017 / Thursday, November 23, 2017
HEURE / TIME :
14 h - 15 h 30 / 2:00 p.m. - 3:30 p.m.
CONFERENCIER(S) / SPEAKER(S) :
Xiannan Li (KSU)
TITRE / TITLE :
Primes in sparse polynomial sequences
LIEU / PLACE :
Concordia University, Library Building, 9th floor, room LB 921-4
RESUME / ABSTRACT :
One particularly difficult class of problems in prime number theory is to prove that certain polynomials take on infinitely many primes values. Typically, these problems become intractable when the sequence given by the polynomial is sparse. In this talk, I will describe some recent work that shows that there are infinitely many primes in a certain sparse sequence.
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Responsable(s) :
Henri Darmon (darmon at math.mcgill.ca)
Adrian Iovita (adrian.iovita at concordia.ca)
Maksym Radziwill (maksym.radziwill at gmail.com)
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