**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.