[Liste-CICMA] Course announcemnent

Daniel Disegni daniel.disegni at gmail.com
Thu Jan 15 12:35:13 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.




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.
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