Past talks (2006-2013)

Department of Mathematics, University of California Riverside

 April 16, 2013 1-2 p.m. Surge 284 Julie Bergner Triangulated categories April 18, 2013 1-2 p.m. Surge 284 Julie Bergner Triangulated categories April 25, 2013 1-2 p.m. Surge 284 Milen Yakimov (Louisiana State University) Quantum cluster algebra structures on quantum nilpotent algebras Abstract. Cluster Algebras and their quantum counterparts play an important role in representation theory, combinatorics and topology. In relation to noncommutative algebra there are several open problems on the existence of cluster algebra structures on certain families of quantized coordinate rings. We will describe a result that proves the existence of quantum cluster algebra structures on a very general, axiomatically defined class of quantum nilpotent algebras. This has a broad range of applications, among which are a proof of the Berenstein-Zelevinsky conjecture for quantum double Bruhat cells, construction of quantum cluster algebra structures on quantum unipotent groups in full generality, and others. May 14, 2013 1-2 p.m. Surge 284 Yuri Bazlov (University of Manchester, United Kingdom) The Kostant Clifford algebra conjecture Abstract. Let $\mathfrak g$ be a complex simple Lie algebra and $\mathfrak h$ its Cartan subalgebra. The Clifford algebra $C(\mathfrak g)$ of $\mathfrak g$ admits a Harish-Chandra map, which turns out to map primitive $\mathfrak g$-invariants in $C(\mathfrak g)$ to $\mathfrak h$. I will discuss a conjecture of Kostant which says that the image of a certain alternating invariant of degree $2m+1$ under this map is the zero weight vector of the simple $(2m+1)$-dimensional module of the principal $\mathfrak{sl}_2$-triple in the Langlands dual of $\mathfrak g$. My original proof of this conjecture was found to be incomplete if $\mathfrak g$ is not of type $A$. A complete proof was subsequently given by Joseph and Alekseev-Moreau. May 16, 2013 1-2 p.m. Surge 284 Mathew Lunde Oral exam May 21, 2013 1-2 p.m. Surge 284 Jonas Hartwig Category $\mathscr O$
 January 29, 2013 1-2 p.m. Surge 284 Jacob West Triangulated categories January 31, 2013 1-2 p.m. Surge 284 Jacob West Triangulated categories February 5, 2013 1-2 p.m. Surge 284 Philip Hackney Triangulated categories February 7, 2013 1-2 p.m. Surge 284 Wee Liang Gan Triangulated categories February 14, 2013 1-2 p.m. Surge 284 Wee Liang Gan Triangulated categories February 19, 2013 1-2 p.m. Surge 284 Liping Li Triangulated categories February 21, 2013 1-2 p.m. Surge 284 Liping Li Triangulated categories February 26, 2013 1-2 p.m. Surge 284 Liping Li Triangulated categories February 28, 2013 1-2 p.m. Surge 284 Liping Li Triangulated categories March 5, 2013 1-2 p.m. Surge 284 Catharina Stroppel (Universität Bonn, Germany, and University of Chicago) (Walled) Brauer algebras and parabolic Kazdhan-Lusztig polynomials Abstract. I this talk I wil briefly recall occurrences of parabolic Kazhdan-Lusztig polynomials of hermitian symmetric cases and related them to the representation theory of Brauer and walled Brauer algebras. In particular we will show that these algebras are Koszul. March 7, 2013 1-2 p.m. Surge 284 Catharina Stroppel (Universität Bonn, Germany, and University of Chicago) Quiver Hecke algebras and $q$-Schur algebras Abstract. In this talk I will introduce the geometry of quiver Hecke algebras and their generalizations to $q$-Schur algebras. As a result we show that decomposition numbers of cyclotomic Schur algebras are governed by Fock space. March 12, 2013 1-2 p.m. Surge 284 Jonas Hartwig Category $\mathscr O$ March 14, 2013 1-2 p.m. Surge 284 Éric Vasserot (Université Paris 7, France) Cherednik algebras and affine category $\mathscr O$ Abstract. We will prove that the category $\mathscr O$ of Cherednik algebras of cyclotomic type is equivalent, as a highest weight category, to the parabolic affine category $\mathscr O$ of type $A$ at a negative level. This implies several conjectures concerning the category $\mathscr O$ of Cherednik algebras.