Algebra and Algebraic Geometry Seminar Fall 2021
The Seminar will take place on Fridays at 2:30 pm, either virtually (via Zoom) or in person, in room B235 Van Vleck.
Algebra and Algebraic Geometry Mailing List
- Please join the AGS mailing list by sending an email to ags+join@g-groups.wisc.edu 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).
COVID-19 Update
As a result of Covid-19, the seminar for this semester will be a mix of virtual and in-person talks. The default Zoom link for the seminar is https://uwmadison.zoom.us/j/9502605167 (sometimes we will have to use a different meeting link, if Michael K cannot host that day).
Fall 2021 Schedule
| date | speaker | title | host/link to talk | |
|---|---|---|---|---|
| September 24 | Michael Kemeny (local, in person) | The Rank of Syzygies | ||
| October 1 | Michael K Brown (Auburn University) | Tate resolutions as noncommutative Fourier-Mukai transforms | Daniel | |
| October 8 | Peter Wei (local) | Geometric Syzygy Conjecture in char p, with reveries from Ogus’ result on a versal deformation of K3 surfaces | Michael | |
| October 15 | ||||
| October 22 | Ritvik Ramkumar (UC Berkeley) | Something about Hilbert schemes, probably | Daniel | |
| October 29 | ||||
| November 5 | Eric Ramos | Equivariant log-concavity | ||
| November 12 | ||||
| November 19 | ||||
| November 26 | Thanksgiving | |||
| December 3 | ||||
| December 10 |
Abstracts
Speaker Name
Michael Kemeny
Title: The Rank of Syzygies
Abstract: I will explain a notion of rank for the relations amongst the equations of a projective variety. This notion generalizes the classical notion of rank of a quadric and is just as interesting! I will spend most of the talk developing this notion but will also explain one result which tells us that, for a randomly chosen canonical curve, you expect all the linear syzygies to have the lowest possible rank. This is a sweeping generalization of old results of Andreotti-Mayer, Harris-Arbarello and Green, which tell us that canonical curves are defined by quadrics of rank four.
Michael Brown
Title: Tate resolutions as noncommutative Fourier-Mukai transforms
Abstract: This is joint work with Daniel Erman. The classical Bernstein-Gel'fand-Gel'fand (or BGG) correspondence gives an equivalence between the derived categories of a polynomial ring and an exterior algebra. It was shown by Eisenbud-Fløystad-Schreyer in 2003 that the BGG correspondence admits a geometric refinement, which sends a sheaf on projective space to a complex of modules over an exterior algebra called a Tate resolution. The goal of this talk is to reinterpret Tate resolutions as noncommutative analogues of Fourier-Mukai transforms, and to discuss some applications.
Peter Wei
Title: Geometric Syzygy Conjecture in char p, with reveries from Ogus’ result on a versal deformation of K3 surfaces
Abstract: We aim to study syzygies of canonical curves in char p. I will briefly introduce how to translate the questions on curves to questions on K3 surfaces, where the Lazarsfeld-Mukai bundle plays a great role. I will show how to use Ogus’ result on a versal deformation of K3 surfaces, to help us resolve the case for a general K3 surface. And finally, I will sketch the proof of Geometric Syzygy Conjecture for even genus curve assuming an effective lower bound on the characteristics.