Tyler Foster: Asymptotics of short intervals on curves over finite fields

Abstract: I will talk about recent joint work with E. Bank in which we formulate and prove an analogue of the short interval conjecture for number fields in the setting of curves over finite fields. This work has several natural and yet-to-be-explored connections to convex geometry, semiring geometry, and some formulations of \(F_1\) geometry. I will try to highlight these connections throughout the talk.