Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics
Subscribe to RSS - Curves Seminar

Curves Seminar

Curves Seminar - Mike Roth (Queen's University)

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.

Curves Seminar - Mike Roth (Queen's University)

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.

Clone of Curves Seminar - Mike Roth (Queen's University)

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.

Curves Seminar - Gregory G. Smith (Queen's University)

Wednesday, January 22nd, 2020

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

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

Title: Green-Lazarsfeld nonvanishing.

Abstract: By exploiting vector bundle techniques for Koszul cohomology, we see how non-trivial geometry leads to non-trivial syzygies.  In particular, this establishes one part of Green’s conjecture.

Curves Seminar - Mike Roth (Queen's University)

Wednesday, December 4th, 2019

Time: 1:30-3:00 p.m Place: Jeffery Hall 319

Speaker: Mike Roth (Queen's University)

Title: Special linear series, the Clifford index, and Green’s conjecture.

Abstract: We will introduce the ideas of linear series, and special linear series on a curve, the notation $g^{r}_{d}$, Clifford’s theorem on special linear series, and state Green’s conjecture for canonically embedded curves.

Curves Seminar - Gregory G. Smith (Queen's University)

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.

Pages