## Effective methods for Darmon points

2013, Aug 25 -- Aug 31

*Organizers:*

F. Fité (U. Bielefeld)

X. Guitart (U. Politècnica de Catalunya)

J.-C. Lario (U. Politècnica de Catalunya)

M. Masdeu (U. Columbia)

V. Rotger (U. Politècnica de Catalunya)

2013, Aug 25 -- Aug 31

*Organizers:*

F. Fité (U. Bielefeld)

X. Guitart (U. Politècnica de Catalunya)

J.-C. Lario (U. Politècnica de Catalunya)

M. Masdeu (U. Columbia)

V. Rotger (U. Politècnica de Catalunya)

In the 90s Henri Darmon introduced the first of a series of conjectural constructions that would generalize the classical method of Heegner points to produce algebraic points on elliptic curves. Since then, many variants and generalizations have been proposed, in which the field of definition of the elliptic curve is allowed to be a number field, or the elliptic curve itself is replaced by more general modular motives.
These constructions are often very explicit and even suited for algorithmic implementations, which calculate the points in concrete examples. The interest of these practical computations is at least threefold:

1. The constructions are conjectural in most of the cases; explicit computations give numerical evidence for the conjectures.

2. If the algorithm is efficient enough it can be used to finding algebraic points which would otherwise stay out of reach.

3. Some of the techniques and algorithms used in these calculations have applications beyond this one, and are of independent interest.

Several of these constructions, however, have not been yet numerically tested and the rationality conjecture is only supported by the analogy with the tested conjectures.

The aim of this workshop is to bridge the gap between theoretical constructions and explicit calculations and to foster new collaborations among the participants, in order to advance in this exciting field.

**Participants**

Amod Agashe

Daniel Barrera

Francesc Castella

Pierre Charollois

Henri Darmon

Lassina Dembele

Mladen Dimitrov

Francesc Fite

Xavier Guitart

Joan-Carles Lario

Alan Lauder

David Loeffler

Matteo Longo

Elisa Lorenzo

Marc Masdeu

Juan Restrepo

Victor Rotger

Mehmet Haluk Sengun

Marco Seveso

Mak Trifkovic

Rodolfo Venerucci

Carlos de Vera

Chris Williams

Sarah Zerbes

**Further Information. **