turkmath.org

Curves over finite fields with many rational points have been of interest for both theoretical reasons and for applications. To obtain such curves with large genus various methods have been employed in the past. One such method is by means of explicit recursive equations and will be the emphasis of this talk. The recursive nature of these towers makes them very special and in fact all good examples have been shown to have a modular interpretation of some sort. In this talk I will try to give an overview of the landscape of explicit recursive towers and their modularity.