Title: Integration, Measures and Relations Between Multiple Zeta Values
Abstract: Throughout all areas of math integration is ubiquitous and provides enormous utility in understanding mathematical concepts - even for many things outside of analysis. In fact, integration often provides just as much information about algebraic objects as studying the objects themselves. So what should we do when we work in a setting which doesn't have integration?
My research seeks to understand relationships between function field multiple zeta values. Classically, one uses an integral to generate such relations, but in the positive characteristic function field setting there is no useful integration theory. In this talk, I will explain why integration fails in this setting. We will also cover a broad overview (aimed at non-expert mathematicians) of function fields and multiple zeta values. Finally, I will explain how my recent work seeks to develop a non-calculus based replacement theory for integration, and how this allows us to recover relations between multiple zeta values.