Algebra and Algebraic Geometry Seminar Fall 2018

From Math
Jump to: navigation, search

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

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

Algebra and Algebraic Geometry Mailing List

  • Please join the AGS Mailing List to hear about upcoming seminars, lunches, and other algebraic geometry events in the department (it is possible you must be on a math department computer to use this link).

Fall 2018 Schedule

date speaker title host(s)
September 7 Daniel Erman Big Polynomial Rings Local
September 14 Akhil Mathew (U Chicago) Kaledin's noncommutative degeneration theorem and topological Hochschild homology Andrei
September 21 Andrei Caldararu Categorical Gromov-Witten invariants beyond genus 1 Local
September 28 Mark Walker (Nebraska) Conjecture D for matrix factorizations Michael and Daniel
October 5
October 12 Jose Rodriguez (Wisconsin) TBD Local
October 19 Oleksandr Tsymbaliuk (Yale) Modified quantum difference Toda systems Paul Terwilliger
October 26 Juliette Bruce Covering Abelian Varieties and Effective Bertini Local
November 2 Behrouz Taji (Notre Dame) TBD Botong Wang
November 9 Rohit Nagpal (Michigan) TBD John WG
November 16 Wanlin Li TBD Local
November 23 Thanksgiving No Seminar
November 30 John Wiltshire-Gordon TBD Local
December 7 Michael Brown TBD Local
December 14 TBD (this date is now open again!) TBD

Abstracts

Akhil Mathew

Title: Kaledin's noncommutative degeneration theorem and topological Hochschild homology

For a smooth proper variety over a field of characteristic zero, the Hodge-to-de Rham spectral sequence (relating the cohomology of differential forms to de Rham cohomology) is well-known to degenerate, via Hodge theory. A "noncommutative" version of this theorem has been proved by Kaledin for smooth proper dg categories over a field of characteristic zero, based on the technique of reduction mod p. I will describe a short proof of this theorem using the theory of topological Hochschild homology, which provides a canonical one-parameter deformation of Hochschild homology in characteristic p.

Andrei Caldararu

Categorical Gromov-Witten invariants beyond genus 1

In a seminal work from 2005 Kevin Costello defined numerical invariants associated to a Calabi-Yau A-infinity category. These invariants are supposed to generalize the classical Gromov-Witten invariants (counting curves in a target symplectic manifold) when the category is taken to be the Fukaya category. In my talk I shall describe some of the ideas involved in Costello's approach and recent progress (with Junwu Tu) on extending computations of these invariants past genus 1.

Mark Walker

Conjecture D for matrix factorizations

Matrix factorizations form a dg category whose associated homotopy category is equivalent to the stable category of maximum Cohen-Macaulay modules over a hypersurface ring. In the isolated singularity case, the dg category of matrix factorizations is "smooth" and "proper" --- non-commutative analogues of the same-named properties of algebraic varieties. In general, for any smooth and proper dg category, there exist non-commutative analogues of Grothendieck's Standard Conjectures for cycles on smooth and projective varieties. In particular, the non-commutative version of Standard Conjecture D predicts that numerical equivalence and homological equivalence coincide for such a dg category. Recently, Michael Brown and I have proven the non-commutative analogue of Conjecture D for the category of matrix factorizations of an isolated singularity over a field of characteristic 0. In this talk, I will describe our theorem in more detail and give a sense of its proof.

Oleksandr Tsymbaliuk

Modified quantum difference Toda systems

The q-version of a Toda system associated with any Lie algebra was introduced independently by Etingof and Sevostyanov in 1999. In this talk, we shall discuss the generalization of this construction which naturally produces a family of 3^{rk(g)-1} similar integrable systems. One of the key ingredients in the proof is played by the fermionic formula for the J-factors (defined as pairing of two Whittaker vectors in Verma modules), due to Feigin-Feigin-Jimbo-Miwa-Mukhin. In types A and C, our construction admits an alternative presentation via local Lax matrices, similar to the classical construction of Faddeev-Takhtajan for the classical type A Toda system. Finally, we shall discuss the geometric interpretation of Whittaker vectors in type A.

This talk is based on the joint work with M. Finkelberg and R. Gonin.

Juliette Bruce

Covering Abelian Varieties and Effective Bertini

I will discuss recent work showing that every abelian variety is covered by a Jacobian whose dimension is bounded. This is joint with Wanlin Li.