BILKENT
ALGEBRA SEMINAR

"Modular Towers of Function
Fields"

By

Alp Bassa

(Sabancı University)

Abstract:  In this talk we will consider the question of how many
rational points a curve over a finite field of large genus can have. One of the
main sources for curves with many points are modular
curves. In fact the first examples of curve with many points and good
asymptotic behaviour given by Ihara and Tsfasman--Vladut--Zink were of this type and many of the interesting
explicit examples of Garcia--Stichtenoth and others
have been shown by Elkies to have a modular
interpretation as well. We will elaborate further on this modularity, show how
it can be used to obtain more insight in explicit optimal towers and sketch a Drinfeld modular interpretation for a new family of towers
of function fields. These towers give examples with large limits over all
non-prime finite fields. (This is joint work with Beelen,
Garcia and Stichtenoth.)

Date:
Monday, March 19, 2012

Time: 15.40-16.30

Place: Mathematics Seminar Room,
SA-141