Wednesday, February 12th, 2020

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

Speaker: Mike Roth (Queen's University)

Title: Lazarsfeld-Mukai bundles.

Abstract: The talk will cover the construction of a particular kind of vector bundle on a K3 surface, obtained by starting with a $g^{1}_{d}$ 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.

Wednesday, January 29th, 2020

Time: 4:00-5:30 p.m Place: Jeffery Hall 319

Speaker: Mike Roth (Queen's University)

Title: An overview of Brill-Noether theory.

Abstract: The object of Brill-Noether theory is to answer the question : which $g^{r}_{d}$’s can a generic curve of genus $g$ have?

The relevance to Green’s conjecture is that this then allows us to compute the Clifford index of a generic curve of genus $g$.

The lecture will be an overview of Brill-Noether theory, including a sketch of the main lines of argument.

Wednesday, January 15th, 2020

Time: 4:00-5:30 p.m Place: Jeffery Hall 319

Speaker: Gregory G. Smith (Queen's University)

Title: Koszul cohomology.

Abstract: We introduce and discuss Koszul cohomology from both an algebraic and geometric perspective. This machinery will eventually help us to understand the syzygies of canonical curves.

Wednesday, November 20th, 2019

Time: 4:00-5:30 p.m Place: Jeffery Hall 319

Speaker: Gregory G. Smith (Queen's University)

Title: Patterns in the Betti tables.

Abstract: We will examine some of the numerical restrictions on the Betti numbers appearing in the minimal free resolution of the homogeneous coordinate ring of a canonical curve. We will also highlight the consequences of these conditions on low genus curves.

Wednesday, November 6th, 2019

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

Speaker: Mike Roth (Queen's University)

Title: Betti tables for canonical curves of genus 5 and 6, III.

Abstract: We will continue the computation of the possible Betti tables of genus 5 curves.