Mathematics Graduate Student Colloquium

MGSC Website: http://math.uci.edu/~mgsc/

Average Cyclicity for Elliptic Curves with Nontrivial Torsion

Luke Fredericks
Monday, December 3, 2018
4:00 pm - 4:50 pm
TBD

Talk Abstract:

Given an elliptic curve E over ℚ , we can reduce (mod p ) for all but finitely many primes p to obtain an elliptic curve over the finite field F _p . There are many natural questions we can ask about the group E ( F _p ) of F _p -rational points. For example: how often is E ( F _p ) a cyclic group? We will discuss the prime counting function

This talk will summarize what is known about this function; in particular, we address the average growth of this function where we average over curves with specified torsion over ℚ .

About the Speaker:

TBA

Refreshments:

Pizza will be served after the talk.