Syzygies and Mirror Symmetry Virtual Seminar

Fall 2025

Tuesdays 1:30-2:30 pm CT

Organizers:

Matthew Ballard, Christine Berkesch, Michael Brown, Daniel Erman, David Favero, Andrew Hanlon, Sheel Ganatra

Background: This seminar was launched in Spring 2024 with the goal of creating new connections among researchers working on the circle of ideas related to multigraded syzygies, homological mirror symmetry, derived categories of toric varieties, and more. The seminar is now part of the FRGMS: Multigraded Commutative Algebra, Toric Varieties, and Homological Mirror Symmetry.

If you are interested in giving such a talk, please fill out this form (you may also want to email one of the organizers directly).

Anyone is welcome to attend this seminar, so please feel free to share this site with anyone you think might be interested.

Logistics: You can sign up for the mailing list here. The zoom link is here or you can use

Meeting ID: 953 1307 7795 and Passcode: RingsHave1

In Spring 2024 and Fall 2024, the seminar focused primarily on expository talks. In Spring 2025, the seminar is changing format, and will feature an array of short talks (20-25 minutes) to provide a snapshot of current research on these topics, and—hopefully—to create new connections. Each week will feature two short talks.

In Fall 2025, the seminar is changing format (again), we plan to run a learning seminar on VGIT and later tackle its connection to mirror symmetry and derived categories.

Sep 9 at 3:30pm CT - Victoria Hoskins (Universitat Duisburg-Essen) Introduction to VGIT

Sep 16 - Pouya Layeghi (UMN) - Mumford Chap 0,1

Print.pdf

Sep 23 - Mykola Sapronov (UMN) - Mumford Chap 2,3

Sep 30 - Dashiell Stevanovich (UMN) - Moduli of Projective Hypersurfaces and Quiver Representations

We will do a brief review of the Hilbert Mumford Criterion and its relationship to stability in GIT problems. We will explore two moduli space examples in depth.

SMS_GIT_Talk_filled_in.pdf

Oct 7 - Isidora Bailly-Hall (UMN) - Intro to Toric GIT

When a subgroup of a torus G acts on affine space C^r, the resulting GIT quotient is toric. In this talk we will follow Cox, Little, and Schenck Chapter 14, beginning by reviewing necessary GIT vocabulary before describing these quotients in the language of toric varieties. Finally, we will introduce the secondary fan and discuss some ways it controls the behavior of GIT quotients as we range over choices of characters.

Isidora Notes.pdf

Oct 14 - Oliver Marcus (UMN) - More on Toric GIT and Wall Crossings

We will continue last week's discussion of toric GIT quotients, drawing from Chapter 15 of Cox, Little, and Schenck. We will begin by reviewing and improving our tools for analyzing GIT quotients given by characters in the secondary fan. We will see how the moving and nef cones of a toric variety relate to the secondary fan. Lastly, we will characterize the relationships between the varieties obtained from chambers of the secondary fan on opposite sides of a wall.

Syzygies and Mirror Symmetry Virtual Seminar

Fall 2025

Tuesdays 1:30-2:30 pm CT

Organizers:

Matthew Ballard, Christine Berkesch, Michael Brown, Daniel Erman, David Favero, Andrew Hanlon, Sheel Ganatra

Sep 9 at 3:30pm CT - Victoria Hoskins (Universitat Duisburg-Essen) Introduction to VGIT

Sep 16 - Pouya Layeghi (UMN) - Mumford Chap 0,1

Sep 23 - Mykola Sapronov (UMN) - Mumford Chap 2,3

Sep 30 - Dashiell Stevanovich (UMN) - Moduli of Projective Hypersurfaces and Quiver Representations

Oct 7 - Isidora Bailly-Hall (UMN) - Intro to Toric GIT

Oct 14 - Oliver Marcus (UMN) - More on Toric GIT and Wall Crossings

Oct 21 - Greg Smith (Queens University) - Introduction to Toric Stacks

Oct 28 - Matthew Ballard (U South Carolina) - VGIT and Derived Categories

Nov 4 - Aimeric Malter (BIMSA) - Toric Exoflops

Nov 11 - Elana Kalashnikov (U Waterloo) - VGIT and Mirror Symmetry

Nov 18 - Jesse Huang (Waterloo) - VGIT and Lagrangian Skeleta

Nov 25 - Thanksgiving week (no seminar)

Dec 4 1:30-2:30 CT - Kimoi Kemboi (Princeton)