# Algebra and Algebraic Geometry Seminar Spring 2019

The seminar meets on Fridays at 2:25 pm in room B235.

Here is the schedule for the previous semester, for the next semester, and for this semester.

## Contents

## Algebra and 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 2019 Schedule

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

January 25 | Daniel Smolkin (Utah) | Symbolic Powers in Rings of Positive Characteristic | Daniel |

February 1 | Juliette Bruce | Asymptotic Syzgies for Products of Projective Spaces | Local |

February 8 | Isabel Vogt (MIT) | Low degree points on curves | Wanlin and Juliette |

February 15 | Pavlo Pylyavskyy (U. Minn) | TBD | Paul Terwilliger |

February 22 | Michael Brown (Wisconsin) | Chern-Weil theory for matrix factorizations | Local |

March 1 | Shamgar Gurevich (Wisconsin) | Harmonic Analysis on GLn over finite fields, and Random Walks | Local |

March 8 | Jay Kopper (UIC) | TBD | Daniel |

March 15 | TBD | TBD | TBD |

March 22 | No Meeting | Spring Break | TBD |

March 29 | Chris Eur (UC Berkeley) | TBD | Daniel |

April 5 | TBD | TBD | TBD |

April 12 | TBD | TBD | TBD |

April 19 | Eloísa Grifo (Michigan) | TBD | TBD |

April 26 | TBD | TBD | TBD |

May 3 | TBD | TBD | TBD |

## Abstracts

### Daniel Smolkin

**Symbolic Powers in Rings of Positive Characteristic**

The n-th power of an ideal is easy to compute, though difficult to describe geometrically. In contrast, symbolic powers of ideals are difficult to compute while having a natural geometric description. In this talk, I will describe how to compare ordinary and symbolic powers of ideals using the techniques of positive-characteristic commutative algebra, especially in toric rings and Hibi rings. This is based on joint work with Javier Carvajal-Rojas, Janet Page, and Kevin Tucker. Graduate students are encouraged to attend!

### Juliette Bruce

**Title: Asymptotic Syzygies for Products of Projective Spaces**

I will discuss results describing the asymptotic syzygies of products of projective space, in the vein of the explicit methods of Ein, Erman, and Lazarsfeld’s non-vanishing results on projective space.

### Isabel Vogt

**Title: Low degree points on curves**

In this talk we will discuss an arithmetic analogue of the gonality of a curve over a number field: the smallest positive integer e such that the points of residue degree bounded by e are infinite. By work of Faltings, Harris--Silverman and Abramovich--Harris, it is well-understood when this invariant is 1, 2, or 3; by work of Debarre--Fahlaoui these criteria do not generalize to e at least 4. We will study this invariant using the auxiliary geometry of a surface containing the curve and devote particular attention to scenarios under which we can guarantee that this invariant is actually equal to the gonality . This is joint work with Geoffrey Smith.