[Liste-CICMA] Course announcement - Topics in number theory

Guillermo Martinez-Zalce martinez at crm.umontreal.ca
Thu Jan 15 16:19:11 EST 2015


Dear all,

This is to announce a graduate course that I will be teaching starting next Wednesday. The details are below.If you know of people who might be interested but are not on this list, please forward this message to them. If you would like to receive further announcements and cannot attend the first lecture, please send me an email.

Best,

Daniel Disegni


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When / where: Wednesdays 2-4.30 pm, room 4336 at the CRM (pavillon Aisenstadt, UdeM)

Course description

The course will cover a variety of topics, with the end goal of explaining the recent paper "Gross-Kudla-Schoen cycles and twisted triple product Selmer groups" by Yifeng Liu, which proves new cases of the Bloch-Kato conjectures relating ranks of Selmer groups to L-functions.
The following topics will be discussed (in varying degree of detail): Kolyvagin's theorem on ranks of elliptic curves; Shimura curves, p-adic uniformization, Ribet's level-raising, the Jacquet-Langlands correspondence, and Bertolini-Darmon's proof of Kolyvagin's result; the Gan-Gross-Prasad conjectures on automorphic periods and their arithmetic analogues; Hilbert modular surfaces, their reduction, the Tate conjecture, and Hirzebruch-Zagier maps.

The course will be an ideal continuation of a seminar held at Concordia in the Fall. However previous attendance to that seminar is not a prerequisite (in fact your instructor would not fulfill that prerequisite). Please feel free to email with any questions.

daniel.disegni at gmail.com

____________________
Guillermo Martinez-Zalce
Responsable des laboratoires
Centre de recherches mathématiques
Université de Montréal
Case postale 6128, Succursale centre-ville
Montréal (Québec)
H3C 3J7
tel: (514) 343-7574
      (514) 398-3826 (mercredis)




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