An activity of an i-MATH Intensive Research Programme
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An activity of an i-MATH Intensive Research Programme |
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| Booklet | |||
| List of participants with lodging arranged through the CRM | |||
| List of participants | |||
| Programme | |||
| Dates: | December 14 to 18, 2009 | ||
| Place: | Centre de Recerca Matemàtica (CRM), Bellaterra, Barcelona, Spain |
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Goals
An interrelated web of conjectures, due, in rough chronological order, to Birch--Swinnerton-Dyer, Tate, Bloch--Beilinson, and Bloch--Kato,connects the arithmetic properties of algebraic cycles (taken modulo some relation, such as rational or algebraic equivalence) with the analytic properties of associated L-functions.
The varieties for which we have the most explicit information --concerning the cycles that live on them, as well as their l-adic cohomology groups and attendant L-functions -- are those that can be related to automorphic forms: Shimura varieties and their relatives.
Studying these examples and exploiting their rich underlying structure has led to a fruitful interaction between arithmetic algebraic geometry and representation theory whose intensity shows no sign of abating.
The simplest case of special cycles on Shimura varieties are the CM points on modular curves; their existence is key to proving the Birch and Swinnerton-Dyer conjecture for elliptic curves of analytic rank at most one.
Besides, the Tate conjectures have been verified in some significant higher dimensional examples involving Shimura varieties on which explicit cycles can be constructed. This is the case for instance of Hirzebruch-Zagier cycles on Hilbert modular surfaces.
Indeed, CM points and Hirzebruch-Zagier cycles have a host of natural generalisations, such as special cycles on Shimura varieties of orthogonal or unitary type. In spite of intense effort that have been deployed in pursuing these generalisations, and the impressive results that have been obtained to date, it can be said that their arithmetic study is still in its infancy and presents many exciting opportunities.
The one-week workshop that we plan to hold in this subject will focus on the following topics:
-- Arithmetic of modular and Shimura curves, and CM points;
-- Special cycles on Shimura varieties of orthogonal and unitary type; relations with singular theta lifts and the Borcherds lift.
-- Beilinson-Kato elements, and other Euler systems.
-- Heights of special cycles, and Arakelov theory.
-- p-adic analogues and their connection with Iwasawa theory and p-adic families of modular forms.
-- Special topological cycles, such as ATR cycles, and their connections with the Stark Conjectures and explicit class field theory.
Scientific Committee
Henri Darmon, McGill University, Montreal
Fred Diamond, King's College of London
Luis Dieulefait, Universitat de Barcelona
Bas Edixhoven, Leiden University
Victor Rotger, Universitat Politècnica de Catalunya
Confirmed Speakers
Jan Bruinier (Darmstadt)
François Brunault (Lyon)
Jose I. Burgos (Barcelona)
Pierre Charollois (Paris)
Christophe Cornut (Paris)
Samit Dasgupta (Santa Cruz, California)
Mladen Dimitrov (Paris)
Tim Dokchitser (Cambridge)
Matthew Greenberg (Calgary)
Benjamin Howard (Boston)
Anton Mellit (Bonn)
Stefan Muller-Stach (Mainz)
Jan Nekovar (Paris)
JeeHoon Park (Montreal)
Robert Pollack (Boston)
Victor Rotger (Barcelona)
Karl Rubin (Irvine)
Marco Seveso (Milano)
Michael Spiess (Bielefield)
Glenn Stevens (Boston)
Eric Urban (New York)
Tonghai Yang (Wisconsin)
Wei Zhang (Harvard)
Registration
Fee: 60 Euros, including participation to the lectures, documentation package, lunch tickets, and coffee breaks.
Deadline for registration and payment: November 15, 2009
| Registration (closed): word file - pdf file |
| Payment: word file - pdf file |
For registration and payment fill out the documents above and follow the instructions there
Accommodation
Participants are encouraged to book their lodging as soon as possible.