Algebra Seminar
(Mon 3:30-4:30pm, Kap 265)
Organizer: Cris Negron
Topics include (but are not limited to):
Algebra, representation theory, algebraic and arithmetic geometry, homotopy theory, and mathematical physics.
| Date | Location | Speaker | Abstract |
|---|---|---|---|
| Jan 19 | Holiday | ||
| Jan 26 | Organizer away | ||
| Feb 2 | |||
| Wed. Feb 11, 2pm | Biman Roy (USC) | Geometric implications of 𝔸1-connectedness Abstract: 𝔸1-homotopy theory, introduced by Morel and Voevodsky, allows us to apply the algebraic topology techniques in algebraic geometry. From the standpoint of homotopy theory of a model category, there is an abstract notion of 𝔸1-connected component sheaf of a variety. It is a natural goal to understand the 𝔸1-connected component sheaf of a variety geometrically and this was initiated by Asok and Morel. They proved that a smooth proper variety X over a field k is 𝔸1-connected if and only if for every finitely generated separable field extension F/k, any two F-points in X can be joined by a chain of 𝔸1F’s in X. In this talk, we will see that if X is an 𝔸1-connected smooth variety over an algebraically closed field k, then X is 𝔸1-uniruled. Thus in particular, if k is of characteristic zero, then X has negative logarithmic Kodaira dimension. We will also see some useful consequences of this result. This is based on my Ph.D. thesis and this is a joint work with Utsav Choudhury. |
|
| Feb 16 | Holiday | ||
| Feb 23 | Nathan Benjamin (USC) [Moved to Mar 23] | ||
| March 2 | Haoyang Liu (UCSB) [Moved to Apr 27] | ||
| March 9 | Mark Ebert (UCLA) | ||
| March 16 | Off | ||
| March 23 | Nathan Benjamin (USC) | Conformal field theory: from magnets to Hodge numbers Abstract: I will introduce the notion of a conformal field theory (CFT), which are quantum field theories at the endpoints of renormalization group flows. CFTs show up in many areas of physics, including second-order phase transitions, string worldsheet theories, and quantum gravity in anti de Sitter space. CFTs also have applications in pure math, and can be thought of as a kind of "generalization" of geometric objects. As an example, I will show how topological invariants of certain manifolds (such as Hodge numbers) are in one-to-one correspondence with a special class of quantum states in a 2d CFT. |
|
| March 30 | Enrico Lampetti (Sorbonne U) | ||
| April 6 | |||
| April 13 | |||
| April 20 | |||
| April 27 | Haoyang Liu (UCSB) |
Mailing list: Contact me if you want to be added to the seminar mailing list.
See our friends at the Geometry seminar (M 2:00 pm) and the Combinatorics seminar (W 2:00 pm).