## AnGeLS (Algebra and Geometry Learning Seminar)

This seminar provides a relaxed environment, in which students and postdocs give talks about various topics in algebraic geometry and related subjects. If you have any questions, contact Franco. You are welcome to suggest topics for the seminar.

### Spring 2020

**Time and place:** Mondays 3:45 - 4:45, Hill 525

- 01/27 Organizational meeting. Also, What's a site?, Ian Coley
- 02/03
**Justin Hoffmann, Topological K-Theory : Bott Periodicity**

The goal of this week's seminar is to understand Bott Periodicity. This talk will introduce the Grothendieck construction, Brown representability theorem, and the concept of a spectrum. At the end of the talk we will discuss the Bott Periodicity Theorem. - 02/03
**Thomas Murrills, Principal G-Bundles: Equivalent Descriptions**

We discuss in detail the equivalence of two particular constructions. Namely, for a topological group G and a topological space B, we construct an equivalence between the classes of principal G-bundles over B and the classes of (G-coherent) sets of transition functions over B. As an application, we use this to show the equivalence between the classes of F-vector bundles over B and the classes of principal GL(n,F)-bundles over B. - 02/03
**Ian Coley, All that's left**

We'll tie up loose ends and recap/complete our discussion on Bott's periodicity.

### Fall 2019

**Time and place:** Tuesdays 2 - 3, in Hill 425

- 10/08 Franco, The derived category of coherent sheaves;

The first few talks will be focused on Angela Gibney's GAeL lecture notes. Here is a tentative speaker list:

- 10/15 Weihong, Moduli spaces of curves;
- 10/22 Vernon, Vector bundles of conformal blocks;
- 10/29 Franco, Geometric interpretations;
- 11/05 Justin, First Chern classes: vanishing, identities, applications;
- 11/12 Justin, First Chern classes: vanishing, identities, applications.

Next, we will focus on this this survey by Colliot-Thélène and this paper by Colliot-Thélène and Ojanguren.

- 11/19 Mihail, Group cohomology;
- 12/03 Saurabh, Birational invariants, purity and the Gersten conjecture.

- 12/10 Ian, Spectral sequences.