Algebra and Algebraic Geometry Seminar Fall 2018

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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.

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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) TBD 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.


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.