Modul: MAT076 Arbeitsgemeinschaft in Codierungstheorie und Kryptographie

## Recursive Towers over Finite Fields

Talk by Prof. Dr. Alp Bassa

Speaker invited by: Prof. Dr. Joachim Rosenthal

**Date:** 25.05.22 **Time:** 15.15 - 16.15 **Room:** Y27H25

Questions on solutions of polynomial equations over finite
fields have a long history and occupy an important place in number
theory. In this talk we will be interested in the particular case,
where the equations define algebraic curves of large genus.
Understanding the number of rational points on such curves has been an
interesting question. As usual, extremal examples play an important
role and in the past, various methods have been employed to construct
high genus curves over finite fields with many rational points. I will
try to give an overview of several of these methods. One particular
construction is by means of explicit recursive towers and will be the
emphasis of this talk. I will present a result (jointly with Beelen,
Garcia and Stichtenoth) on towers over non-prime finite fields, and a
result (jointly with Ritzenthaler) over prime fields.

(**This eSeminar will also be live-streamed on Zoom, using the same meeting details as previous seminars. If you do not have meeting details, please contact simran.tinani@math.uzh.ch **)