Seminar

Intro to Proof Assistants, Examples with Lean

In this talk, we will explore the practical uses of a proof assistant for mathematicians. In particular, we will learn how to formalize a variety of propositions in the proof assistant Lean 4. Through these examples, we will learn how to convert our familiar strategies into the different proof tactics which have been implemented in Lean. Additionally, we will discuss why they are called proof assistants and the different ways that they make proving things easier. Finally, we’ll touch on some theory behind proof assistants and their role in modern mathematics.

Motivic Classes of Varieties and Stacks with Applications to Higgs Bundles

In this talk, we will first discuss the motivations for motivic classes coming from point counting over finite fields. Then we will give the definitions of the motivic classes of varieties, in particular we explain that an extra relation is needed in finite characteristic. We will introduce symmetric powers and motivic zeta functions that are universal versions of local zeta functions.