*2017-2018 Academic Year*

Pretalks begin an hour earlier in LC 317R (unless otherwise indicated)

Date |
Room |
Speaker |
Title |
Host |

Aug 25 3:30pm |
LC 317R | Jesse Kass(University of South Carolina) |
How to count lines on the cubic surface arithmetically?(No pretalk) |
(local) |

Aug 28 3:30pm |
LC 407 |
Blake Farman(University of South Carolina) |
Kernels for Noncommutative Projective Schemes(No pretalk) |
(local) |

Labor Day | ||||

Sep 25 3:30pm |
LC 317R | - |
- |
- |

Oct 2 3:30pm |
LC 317R | - |
- |
- |

Oct 9 3:30pm |
LC 317R | Bastian Haase(Emory University) |
Gerbe patching over arithmetic curves with a view towards homogeneous spaces |
Duncan |

Oct 16 3:30pm |
LC 317R | - |
- |
- |

Fall Break | ||||

Oct 23 3:30pm |
LC 317R | - |
- |
- |

Oct 30 3:30pm |
LC 317R | - |
- |
- |

Nov 6 3:30pm |
LC 317R | Dustin Cartwright(University of Tennessee) |
TBA |
Duncan |

Nov 13 3:30pm |
LC 317R | - |
- |
- |

Nov 20 3:30pm |
LC 317R | - |
- |
- |

Thanksgiving Break | ||||

Nov 27 3:30pm |
LC 317R | - |
- |
- |

Dec 4 3:30pm |
LC 317R | - |
- |
- |

Abstracts

**Blake Farman** - **Noncommutative projective schemes and DG categories**

In their 1994 paper, Noncommutative Projective Schemes, Michael Artin and J.J. Zhang introduce a generalization of usual projective schemes to the setting of not necessarily commutative algebras over a commutative ring. Gonçalo Tabuada in 2005 endows the category of differential graded categories with the structure of a model category and in 2007 Toën shows that its homotopy category is symmetric monoidal closed. In this talk, we’ll give a brief overview of these results, adapting Artin and Zhang’s noncommutative projective schemes for the language of DG categories, and discuss a “geometric” description of this internal Hom for two noncommutative projective schemes.

**Bastian Haase** - **Gerbe patching over arithmetic curves with a view towards homogeneous spaces**

We will discuss patching techniques and local-global principles for gerbes over arithmetic curves. The patching setup is the one introduced by Harbater, Hartmann and Krashen. The results obtained for gerbes can be viewed as a 2-categorical analogue on their results for torsors. Along the way, we also discuss bitorsor patching and local global principles for bitorsors. As an application of these results, we will study local-global principles for homogeneous spaces through their quotient stacks.

**Pretalk: Field Patching**

In this talk, we will give an introduction to the patching technique introduced by Harbater, Hartmann and Krashen. This technique allows to study algebraic objects such as quadratic forms or central simple algebras over a fixed field via studying the same objects over a finite system of overfields. After discussing the general framework, we will focus on the case of arithmetic curves and discuss a couple of recent results obtained via this technique.

**Jesse Kass** - **How to count lines on the cubic surface arithmetically?**

A celebrated 19th century result of Cayley and Salmon is that a smooth cubic surface over the complex numbers contains exactly 27 lines. Over the real numbers, the number of lines on a smooth cubic surface depends on the surface, but Segre showed that a certain signed count of lines is the same for such surfaces. In my talk, I will explain Segre’s result and then extend that result to an arbitrary field. This is an application of A1-homotopy theory.

All work is joint with Kirsten Wickelgren.