## Curves Seminar

### Wednesday, February 5th, 2020

**Time:** 4:30-5:30 p.m ** Place:** Jeffery Hall 319

**Speaker:** Mike Roth (Queen's University)

**Title:** K3 surfaces and Lazarsfeld-Mukai bundles.

**Abstract:** The talk will be a short introduction to some aspects of K3 surfaces, including their relation with canonical embeddings of curves, as well as details of the construction of a particular kind of vector bundle on a K3 surface, obtained by starting with a $g^{r}_{d}$ on a curve on that surface.

This vector bundle construction appeared in Lazarsfeld’s proof of the Petri conjecture, but has also been one of the main starting points for investigating Green’s conjecture. In particular, it will be used in future lectures giving a recent proof due to Kemeny of Green’s conjecture for generic curves of even genus.