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Workshop

Special values of Rankin L-series December 10, 2001 - December 14, 2001
Registration Deadline: December 14, 2001 almost 18 years ago
To apply for Funding you must register by: September 10, 2001 over 18 years ago
Parent Program: --
Organizers Henri Darmon and Shouwu Zhang
Speaker(s)

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Description
The goal of this workshop is to survey recent developments growing out of the landmark work of Gross and Zagier on the special vlaues of Rankin L-series, and their arithmetic applications. The lectures in the workshop will be organised around 5 main themes related to the formula of Gross and Zagier. 1. History and overview of the Gross-Zagier formula (three lectures) Lecturers: Bryan Birch and Benedict Gross 2. The complex Gross-Zagier formula (three lectures) Lecturers: Benedict Gross and Shouwu Zhang 3. Anticyclotomic p-adic L-functions (two lectures) Lecturers: Massimo Bertolini and Vinayak Vatsal 4. Stark-Heegner points (three lectures) Lecturers: Harold Stark and Henri Darmon 5. Higher dimensional Gross-Zagier formulae (three lectures) Lecturers: Steven Kudla and Richard Borcherds Invited participants include: M. Bertolini, B. Birch, R. Borcherds, C. Cornut, H. Darmon, N. Elkies, D. Goldfeld, B.H. Gross, A. Iovita, K. Keating, S. Kudla, A. Pal, A. Rajaei, H. Stark, D. Ulmer, V. Vatsal, T. Yang, S. Zhang Group Photo of the event participants
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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To apply for funding, you must register by the funding application deadline displayed above.

Students, recent Ph.D.'s, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

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Schedule, Notes/Handouts & Videos
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Dec 10, 2001
Monday
09:15 AM - 10:45 AM
  Heegner points: The beginnings
Bryan Birch
10:45 AM - 02:00 PM
  Heegner points and Rankin L-series, 1980-1987
Benedict Gross (Harvard University)
02:00 PM - 03:00 PM
  The origins of conjectures on derivatives of L-functions at s=0
Harold Stark
Dec 11, 2001
Tuesday
09:00 AM - 10:30 AM
  CM points and arithmetic of modular elliptic curves: Variants, computations and conjectures
Noam Elkies (Harvard University)
10:30 AM - 02:00 PM
  The Gauss class number problem
Dorian Goldfeld
02:00 PM - 03:30 PM
  Stark-Heegner points
Henri Armon
03:30 PM - 04:30 PM
  Uniform distribution of Heegner points
Vinayak Vatsal
Dec 12, 2001
Wednesday
09:00 AM - 10:30 AM
  Arithmetic of elliptic curves over anticyclotomic towers
Massimo Bertolini
10:30 AM - 02:00 PM
  Euler systems and Stark-Heegner points
Henri Darmon (McGill University)
02:00 PM - 03:30 PM
  The Gross-Kohnen-Zagier theorem in higher dimensions
Richard Borcherds (University of California, Berkeley)
03:30 PM - 04:30 PM
  Mazur’s conjecture through the Andre-Oort conjecture
Christophe Cornut
Dec 13, 2001
Thursday
09:00 AM - 10:30 AM
  Heegner points in the context of representation theory
Benedict Gross (Harvard University)
10:30 AM - 02:00 PM
  The kernel for Rankin-Selberg convolution
Shou-Wu Zhang (Princeton University)
02:00 PM - 03:30 PM
  Special cycles and derivatives of Eisenstein series
Stephen Kudla (University of Toronto)
03:30 PM - 04:30 PM
  Gross-Zagier theorems and the conjecture of Birch and Swinerton-Dyer over function fields
Douglas Ulmer (University of Arizona)
Dec 14, 2001
Friday
09:00 AM - 10:30 AM
  The geometric pairing for CM-points
Shou-Wu Zhang (Princeton University)
10:30 AM - 01:00 PM
  Derivatives of p-adic L-functions, Heegner cycles and monodromy modules attached to modular forms
Adrian Iovita (Concordia University)
01:00 PM - 02:30 PM
  On derivatives of Eisenstein series and Faltings’ height
Tonghai Yang (University of Wisconsin-Madison)
02:30 PM - 03:30 PM
  Heegner cycles on moduli of D-elliptic sheaves
Ambrus Pal