Algebra and Algebraic Geometry Seminar Fall 2019

The seminar meets on Fridays at 2:25 pm in room B235 Van Vleck.

Here is the schedule for the previous semester, for the next semester, and for this semester.

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Fall 2019 Schedule

date	speaker	title	host(s)
September 6	Yuki Matsubara	On the cohomology of the moduli space of parabolic connections	Dima
September 13	Juliette Bruce	Semi-Ample Asymptotic Syzygies	Local
September 20	Michael Kemeny	The geometric syzygy conjecture	Local
September 27
October 4
October 11
October 18	Kevin Tucker (UIC)
October 25
November 1	Michael Brown	TBD	Local
November 8	Patricia Klein
November 15
November 22	Daniel Corey	Topology of moduli spaces of tropical curves with low genus	Local
November 29		Thanksgiving Break
December 6			Reserved (Matroids Day)
December 13

Abstracts

Yuki Matsubara

On the cohomology of the moduli space of parabolic connections

We consider the moduli space of logarithmic connections of rank 2 on the projective line minus 5 points with fixed spectral data. We compute the cohomology of such moduli space, and this computation will be used to extend the results of Geometric Langlands correspondence due to D. Arinkin to the case where the this type of connections have five simple poles on ${\mathbb P}^1$.

In this talk, I will review the Geometric Langlands Correspondence in the tamely ramified cases, and after that, I will explain how the cohomology of above moduli space will be used.

Juliette Bruce

Semi-Ample Asymptotic Syzygies

I will discuss the asymptotic non-vanishing of syzygies for products of projective spaces, generalizing the monomial methods of Ein-Erman-Lazarsfeld. This provides the first example of how the asymptotic syzygies of a smooth projective variety whose embedding line bundle grows in a semi-ample fashion behave in nuanced and previously unseen ways.