Date & Time: Monday, August 04, 2008, 12:40-13:40.
Venue: Ramanujan Hall
Title: Towers of Algebraic Function Fields of One Variable Over Finite Fields
Speaker: Habeeb Basha Syed, IIT Bombay
Abstract: We will discuss algebraic curves over finite fields with many points. More precisely, given a finite field F with q elements, we consider the ratio of the number of places of an algebraic function field of one variable over F to its genus. The limit superior of such ratios is bounded above by the well-known Drinfeld-Vladut bound. Sequences of function fields where this bound is attained are called asymptotically optimal towers, while those where the limit exists and is positive are called asymptotically good towers. We will discuss constructions of such towers, with particular emphasis on the so called recursive towers.