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)	TBD	Daniel
October 25	Reserved		Dima
November 1	Michael Brown	Standard Conjecture D for Matrix Factorizations	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.

Michael Brown

Standard Conjecture D for Matrix Factorizations

In 1968, Grothendieck posed a family of conjectures concerning algebraic cycles called the Standard Conjectures. They have been proven in some special cases, but they remain open in general. In 2011, Marcolli-Tabuada realized two of these conjectures as special cases of more general statements, involving differential graded categories, which they call Noncommutative Standard Conjectures C and D. The goal of this talk is to discuss a proof, joint with Mark Walker, of Noncommutative Standard Conjecture D in a special case which does not fall under the purview of Grothendieck's original conjectures: namely, in the setting of matrix factorizations.

Notes

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