Darmon points: algorithms and numerical evidence

Darmon points are a collection of conjectural generalizations of Heegner
points on modular elliptic curves. Algorithms for their effective
calculation are useful for gathering numerical evidence supporting their
conjectured properties. In addition, in some cases they can be used in
practice as very efficient methods for computing algebraic points in such
elliptic curves. In this talk I will recall two constructions of Darmon
points in different settings, and the algorithms of Darmon-Logan and
Darmon-Green-Pollack that allow for their computation in certain elliptic
curves. I will also present some joint work with Marc Masdeu that extends
these algorithms to a wider class of curves and allows to obtain new
numerical evidence for the constructions.