Title:
Points of prime order on elliptic curves over number fields -- a
progress report

Abstract: 
Continuing the topic of my previous talk, we discuss how we
can use some further ideas to determine (or approximate) the set S(d)
of prime numbers occurring as orders of points on elliptic curves over
number fields of degree for d > 6. We also show how certain conjectural
statements on modular forms would imply quite strong statements on the
structure of these sets when d is large.