**Special Seminar**

Come join us **Wednesday,**** February 14, 2018 at 12 pm in RM 507, Professor Chao Li**** (Columbia University) will ****be giving a special lecture about “Elliptic Curves, Heegner Points, and Beyond”.**

**Abstract**

An elliptic curve is a plane curve defined by a cubic equation. Determining whether such an equation has infinitely many rational solutions has been a central problem in number theory for centuries, which led to the celebrated conjecture of Birch and Swinnerton-Dyer. We will start with a history of this problem and then discuss our recent work (with D. Kriz) on certain families of elliptic curves (such as y^2=x^3-d), which in particular proves a conjecture of Goldfeld. Our approach uses Heegner points and their deep connection with L-functions. We will explain these key ingredients and ideas. If time permits, we will also illustrate a framework to go beyond the case of Heegner points and to build a connection with L-functions of more general symplectic motives.

**Mathematics Hall, Room 507**

**Wednesday,**** February 14, 2018 at 12 pm**