# Questions About the Reductions Modulo Primes of an Elliptic Curve

 MEMBERS SEMINAR Topic: Questions About the Reductions Modulo Primes of an Elliptic Curve Speaker: Alina Carmen Cojocaru Affiliation: University of Illinois at Chicago; Member, School of Mathematics Date: Monday, December 13 Time/Room: 2:00pm - 3:00pm/S-101

Many remarkable questions about prime numbers have natural analogues in the context of elliptic curves. Among them, Artin's primitive root conjecture, the twin prime conjecture, and the Schinzel hypothesis have inspired a broad family of conjectures regarding the behavior of the reductions modulo primes of an elliptic curve over Q. I will give an overview of such questions and progress made towards their resolution.