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 11, 2pm | Mark Ebert (UCLA) | Higher tensor products for sl(2) Abstract: Webster famously introduced a categorification of tensor products of simple representations for general Kac-Moody algebras and used them to categorify the Reshetikhin–Turaev invariants. While we can categorify tensor products of representations, the ability to define an explicit "higher" tensor product of categorified representations of Kac-Moody algebra has still not been fully realized. Rouquier defined a general tensor 2-product operation for 2-representations of Kac-Moody algebras in an infinity-categorical setting, and conjectures that these agree with Webster's 2-representations. In joint work with Raphael Rouquier, we construct a model for the tensor product of the regular 2-representation of sl2+ with the vector 2-representation and show that it agrees with the 2-representation of Webster, partially proving Rouquier's conjecture. Our model has the same starting point as that of the minimal model of McMillan, but our use of an infinite family of generators makes our model significantly simpler, which we use to prove the equivalence. |
|
| 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. |
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| 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).