**Date & Time:** January 21, 2011; 15:00-16:00.

**Venue:** Ramanujan Hall

**Title : **Towers of algebraic function fields

**Speaker:** Prof. Peter Beelen,
Technical University of Denmark

**Abstract:** Goppa's ideas from the 1980's allow for the construction of
asymptotically good families of codes using algebraic curves defined
over a finite field. Motivated by this, several constructions emerged of
curves defined over a finite field having many rational points. Historically,
the oldest of these constructions use modular curves. Later, a more
elementary way of constructing families of curves with many rational
points emerged using a recursive description. This construction is
usually given in the language of function fields. Some of these ideas were
discussed in the previous talk. In this talk I will begin with a rapid overview
of the previous talk and then explain the connection between the theory
of modular curves and recursively defined towers of function fields.