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.