# Algebra and Algebraic Geometry Seminar Fall 2021

The Virtual Seminar will take place on Fridays at 2:30 pm via Zoom. We will also link to relevant or interesting Zoom talks outside of the seminar.

## Contents

## 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) | The Rank of Syzygies | ||

October 1 | Michael K Brown (Auburn University) | Something about toric varieties, probably | Daniel | |

October 8 | Peter Wei (local) | TBD (talk will be about results of Ogus on K3 surfaces in char p and syzygies) | 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*.