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.