**Wednesday, Dec 4, 2-3pm ** at

Science Center 507

The Snapshots of Math at Harvard aims to bring people with different research directions together. Each talk is 15 minutes long and is intended to introduce a topic to mathematicians outside the speaker's field. The goal is to exchange broad ideas and foster new mathematical contacts. Everyone is encouraged to discuss with the speakers after the seminar!

**Alex Cowan**

**Title:** Three stories from arithmetic statistics
**Abstract:** This talk will be about three simple-ish problems from the subfield of number theory called "arithmetic statistics". Something satisfying can be said about all three problems, and they're all very popular research topics today. I'll namedrop 5 things that number theorists talk about a lot: elliptic curves, modular forms, Galois representations, the Riemann hypothesis, and the Birch and Swinnerton-Dyer conjecture, and I'll also talk briefly about the work I've done.

**Elana Kalashnikov**

**Title:** Mirror symmetry for quiver flag varieties and their subvarieties
**Abstract:** Smooth Fano varieties of dimension less than three are classified; in dimension four and beyond this is an important open question. I'll talk about the role of mirror symmetry in the Fano classification program and explain why quiver flag varieties are a useful testing ground for the theory.

**Dori Bejleri**

**Title:** Compactifying moduli spaces
**Abstract:** One of the basic goals of geometry is to classify various geometric structures of interest. In algebraic geometry, the set of geometric structures often assemble into a parameter space or moduli space M whose points parametrize the structures of interest and whose local geometry reflects the notion of these structures varying continuously in families. Thus the classification problem in algebraic geometry often becomes the problem of understanding the geometry of the single space M. For many applications, one would like M to be compact. I will introduce some of the ideas that go into constructing compactifications of moduli spaces and applications of these compactifications, focusing on the case of the moduli space M_g of genus g curves. I will maybe say something about moduli spaces of higher dimensional varieties.

**Organizers:** Mandy Cheung (mwcheung@math.harvard.edu)