Seminar: Park -- Totality of rational points on modular curves

Title: Totality of rational points on modular curves 

Presented by: June Park

Abstract: People want to count elliptic curves over global fields such as the field Q of
rational numbers or the field Fq(t) of rational functions over the finite field Fq.  To
this end, we consider the fact that each E/K corresponds to a K-rational point on the
fine moduli stack Mbar_{1,1} of stable elliptic curves, which in turn corresponds to a
rational curve on Mbar_{1,1}.  In this talk, I will explain the exact counting formula
for all elliptic curves over Fq(t) along with an explanation for the geometric origin of
lower order main terms, as well as basic generalities, relevant ideas and methods.