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Vyjayanthi Chari
vyjayanc at ucr.edu |
Wee Liang Gan
wlgan at math.ucr.edu | Jacob Greenstein
jacobg at ucr.edu |
| November 24, 2009 | JOINT WITH ALGEBRAIC GEOMETRY SEMINAR | ||
| 12:40-1:30 p.m. | Surge 284 |
Andrei Caldararu (University of Wisconsin, Madison)
The Duflo conjecture and the Ext algebra of branes Abstract. The Duflo theorem is a statement in Lie theory which allows us to compute the ring structure of the center of the universal enveloping algebra of a finite-dimensional Lie algebra. A categorical version of it was used by Maxim Kontsevich to give a spectacular proof of the so-called "Theorem on complex manifolds," which computes the multiplicative structure of Hochschild cohomology of a complex manifold in terms of the algebra of polyvector fields. In Lie theory there are also more general Duflo-type statements (mostly conjectural), which study the case of a pair (Lie algebra, Lie subalgebra). I will explain how these translate into conjectures about the multiplicative structure of the Ext-algebra of the structure sheaf of a complex submanifold of a complex manifold, and how from this interaction we can hope to gain new insights into both algebraic geometry and Lie theory. (Based on discussions with Damien Callaque.) | |
| December 1, 2009 | |||
| 1-2 p.m. | Surge 284 |
Nathan Manning
TBA | |
| December 3, 2009 | |||
| 1-2 p.m. | Surge 284 |
David Jordan (MIT)
Quantum D-modules and higher genus braid groups Abstract. One motivation for studying quantum groups and braided tensor categories is that they provide a method for constructing representations of the braid groups of type An. It is natural to ask what extra structure on a braided tensor category is required to yield back representations of higher genus braid groups, for example the so-called double affine braid groups, which are π1 of the configuration space of points on an elliptic curve. In this talk we explain that in types An and BCn, the algebra D of quantum differential operators provides this extra structure; more precisely, for any (quantum) D-module, we construct representations of elliptic braid groups of types An and BCn. Connections to classical Lie theory are provided via the theory of double affine Hecke algebras and their degenerations. The BCn constructions we describe are joint work with Xiaoguang Ma. | |
| September 29, 2009 | ||
| 12:40-2 p.m. | Surge 284 | Irfan Bagci
Cohomology and support varieties I Abstract. The talk will start with an introduction to cohomology, support varieties for finite groups over a field of positive characteristic. After that we will discuss support variety theories for algebraic structures other than finite groups such as restricted Lie algebras, algebraic groups, quantum groups and Lie superalgebras. |
| October 1, 2009 | ||
| 12:40-2 p.m. | Surge 284 | Irfan Bagci
Cohomology and support varieties II Abstract. In this second talk we will discuss cohomology and support varieties for Lie superalgebras over the field of complex numbers. I will focus on examples and present some results joint with Jonathan Kujawa and Daniel Nakano. |
| October 6, 2009 | ||
| 1-2 p.m. | Surge 284 | Christian Kassel (CNRS, Institut de Recherche
Mathématique Avancée, Strasbourg, France)
Drinfeld twists and finite groups |
| October 13, 2009 | ||
| 12:40-2 p.m. | Surge 284 |
Eliana Zoque Lopez
On the variety of almost commuting nilpotent matrices Abstract. We study the variety of n by n matrices with commutator of rank at most one. We describe its irreducible components; two of them correspond to the pairs of commuting matrices, and n-2 components of smaller dimension corresponding to the pairs of rank one commutator. In our proof we define a map to the zero fiber of the Hilbert scheme of points and study the image and the fibers. |
| October 15, 2009 | ||
| 12:40-2 p.m. | Surge 284 |
Eliana Zoque Lopez
On the variety of almost commuting nilpotent matrices |
| October 20, 2009 | ||
| 12:40-2 p.m. | Surge 284 |
Jacob Greenstein
Quivers, Hall algebras and quantum groups I |
| October 22, 2009 | ||
| 12:40-2 p.m. | Surge 284 |
Jacob Greenstein
Quivers, Hall algebras and quantum groups II |
| October 27, 2009 | ||
| 12:40-2 p.m. | Surge 284 |
Jacob Greenstein
Quivers, Hall algebras and quantum groups III |
| November 5, 2009 | ||
| 1-2 p.m. | Surge 284 |
Qingtao Chen (University of Southern California)
Quantum invariants of links Abstract. The colored HOMFLY polynomial is a quantum invariant of oriented links in S3 associated with a collection of irreducible representations of each quantum group Uq(slN) for each component of the link. We will discuss in detail how to construct these polynomials and their general structure. Then we will discuss the new progress, Labastida-Marino-Ooguri-Vafa conjecture. The LMOV conjecture also gives the application of Lichorish-Millet type formula for links. The corresponding theory of colored Kauffman polynomials associated to quantum group Uq(so2N+1) and orthogonal version of the LMOV conjecture can also be developed in a same fashion by using more complicated algebra structures. |
| November 12, 2009 | ||
| 1-2 p.m. | Surge 284 |
Fedor Malikov (University of Southern California)
What is a chiral algebra? Abstract. This talk is intended as an elementary and informal introduction to the Beilinson-Drinfeld notion of a chiral algebra. |
