Martin Bishop (UW)

PDL C-38

**Preseminar 1:45-2:15**

**Title**:What are Chow rings and what do they tell us?

**Abstract:**

We will define and give intuition for the Chow ring of a scheme, and then discuss how this definition can be extended to a broader class of objects: quotient stacks.

**Seminar 2:30-3:20**

**Title**:Towards the integral Chow ring of \overline M_{1,3}

**Abstract:**

Chow rings give a way to algebraically track the geometric structure of a space. Chow rings were classically defined for varieties and then schemes. We will give of an exposition of how to extend the definition to quotient stacks, and compute the integral Chow rings of \overline M_{1,1} and \overline M_{1,2}. We will then go over recent progress made towards computing the integral Chow ring of \overline M_{1,3}.