Algebra and Algebraic Geometry Seminar Fall 2019

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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) TBD Daniel
October 25 Reserved Dima
November 1 Michael Brown TBD Local
November 8 Patricia Klein TBD Daniel
November 15 Reserved TBD (Jose)
November 22 Daniel Corey Topology of moduli spaces of tropical curves with low genus Local
November 29 No Seminar Thanksgiving Break
December 6 RESERVED 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.


Michael Kemeny

The geometric syzygy conjecture

A famous classical result of M. Green asserts that the ideal sheaf of a canonical curve is generated by quadrics of rank four. Extending this to higher relations, one arrives at the so-called Geometric Syzygy Conjecture, stating that extremal linear syzygies are spanned by those of the lowest possible rank. This conjecture further provides a geometric interpretation of Green's conjecture for canonical curves. In this talk, I will outline a proof of the Geometric Syzygy Conjecture in even genus, based on combining a construction of Ein-Lazarsfeld with Voisin's approach to the study of syzygies of K3 surfaces.


Notes

Because of exams and/or travel, Daniel is unable to attend seminars on Oct 11, Oct 18, Nov 15, and Dec 13.