# Algebraic Geometry Seminar Spring 2016

The seminar meets on Fridays at 2:25 pm in Van Vleck B113.

The schedule for the previous semester is here.

## Contents

## 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).

## Spring 2016 Schedule

date | speaker | title | host(s) |
---|---|---|---|

January 22 | Tim Ryan (UIC) | Moduli Spaces of Sheaves on \PP^1 \times \PP^1 | Daniel |

January 29 | Local | ||

February 5 | Botong Wang (Wisconsin) | Topological Methods in Algebraic Statistics | Local |

February 12 | Jay Yang (Wisconsin) | Random Toric Surfaces | Local |

February 19 | Daniel Erman (Wisconsin) | Supernatural Analogues of Beilinson Monads | |

February 26 | TBD | ||

March 4 | Claudiu Raicu (Notre Dame) | TBA | Steven |

March 11 | Eric Ramos (Wisconsin) | Local Cohomology of FI-modules | Local |

March 18 | Spring break | ||

March 25 | TBD | ||

April 1 | TBD | ||

April 8 | TBD | ||

April 15 | TBD | ||

April 22 | TBD | ||

April 29 | David Anderson (Ohio State) | TBA | Steven |

May 6 | TBD |

## Abstracts

### Tim Ryan

Moduli Spaces of Sheaves on \PP^1 \times \PP^1

In this talk, after reviewing the basic properties of moduli spaces of sheaves on P^1 x P^1, I will show that they are $\mathbb{Q}$-factorial Mori Dream Spaces and explain a method for computing their effective cones. My method is based on the generalized Beilinson spectral sequence, Bridgeland stability and moduli spaces of Kronecker modules.

### Botong Wang

Topological Methods in Algebraic Statistics

In this talk, I will give a survey on the relation between maximum likelihood degree of an algebraic variety and it Euler characteristics. Maximam likelihood degree is an important constant in algebraic statistics, which measures the complexity of maximum likelihood estimation. For a smooth very affine variety, June Huh showed that, up to a sign, its maximum likelihood degree is equal to its Euler characteristics. I will present a generalization of Huh's result to singular varieties, using Kashiwara's index theorem. I will also talk about how to compute the maximum likelihood degree of rank 2 matrices as an application.

### Daniel Erman

Supernatural analogues of Beilinson monads

First I will discuss Beilinson's resolution of the diagonal and some of the applications of that construction including the notion of a Beilinson. Then I will discuss new work, joint with Steven Sam, where we use supernatural bundles to build GL-equivariant resolutions supported on the diagonal of P^n x P^n, in a way that extends Beilinson's resolution of the diagonal. I will discuss some applications of these new constructions.