**Date & Time:** Friday, January 03, 2014, 16:00-17:00.

**Venue:** Ramanujan Hall

**Title:** Stark-Heegner/Darmon points on elliptic curves over totally real fields

**Speaker:** Amod Agashe, Florida State University

**Abstract:** The classical theory of complex multiplication gives certain points on
elliptic curves defined over quadratic imaginary fields called Heegner points.
These points played a crucial role in the resolution of the Birch and
Swinnerton-Dyer conjecture when the analytic rank of the elliptic curve is zero
or one. Darmon and others have given conjectural generalizations of Heegner
points to give points defined over certain fields other than quadratic imaginary
fields (conjecturally); these points are called Stark-Heegner points or Darmon
points. We will give a survey of what is known, including a result of ours with
Mak Trifkovic.