Advanced Course on

Algebraic Cycles, Modular Forms, and Rational Points on Elliptic Curves

An activity of an i-MATH Intensive Research Programme

Group Picture
Programme NEW!
List of participants with lodging arranged through the organisation (at Vila Universitària 2, UAB Campus, Bellaterra) NEW!
List of participants
Dates:	December 9 to 12, 2009
Place:	Centre de Recerca Matemàtica (CRM), Bellaterra, Barcelona, Spain	How to reach the CRM

Goals

The theme of this course is  the construction of algebraic points on elliptic curves from special points and higher-dimensional cycles on Shimura varieties and closely related objects.  We will provide background for, explain,  and, time permitting, expand further on  the results that are proven   in the two articles

M. Bertolini, H. Darmon, and K. Prasanna, "Generalised Heegner cycles and p-adic Rankin L-series";

M. Bertolini, H. Darmon, and K. Prasanna, "Chow-Heegner points on CM elliptic curves and values of p-adic L-series".

Some of the topics that will be discussed will include:

1. Classical Heegner points

2. Algebraic cycles. Complex and p-adic Abel-Jacobi maps

3. The differential operators of Shimura-Maass and Atkin-Serre on nearly holomorphic and p-adic modular forms

3. p-adic L-series attached to CM Hecke characters, and to Rankin convolutions

4. A p-adic Gross-Zagier formula for generalised Heegner cycles

5. (Time permitting) Other topics such as: ATR cycles on Hilbert modular varieties, or special cycles on Shimura varieties of orthogonal or unitary type

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)

Speakers

Registration and Financial Support

The CRM offers a limited number of grants covering registration and accommodation addressed to young researchers. You will need to follow these steps:

• Register to the activity.
• Apply for financial support. (Applicants will need to send by email a curriculum vitae to the email adress: accycles@crm.cat. Please note that no applications will be taken into consideration otherwise)
• Pay the registration fee.

You will be informed as soon as possible whether support is available.

Registration fee: 300 Euros, including participation to the lectures, documentation package, a copy of the course notes, lunch tickets, a social dinner, a cultural activity, and coffee breaks.

For registration and payment fill out the documents above and follow the instructions there

Accommodation

Participants awarded with accommodation grants will have their lodging arranged through the organisation. The remaining participants are encouraged to book their lodging as soon as possible.

• Information on accommodation options for participants

For further information, please contact the CRM Administration.