Yiyang Li (Shanghai University of Engineering Science)

Title: Filtrations in Modular Representations of Reductive Lie Algebra
Abstract: Let $G$ be a connected reductive group $G$ over an algebraically closed field $k$ of prime characteristic $p$, and $g=Lie(G)$. In this presentation, we study representations of the reductive Lie algebra $g$ with $p$-character $\chi$ of standard Levi-form associated with an index subset $I$ of simple roots. With aid of support variety theory we prove a theorem that a $U_\chi(g)$-module is projective if and only if it is a strong ``tilting" module, i.e. admitting both $Z_Q$- and $Z^{w^I}_Q$-filtrations . Then by analogy of the arguments of Andersen-Kaneda for $G_1T$-modules, we construct so-called Andersen-Kaneda filtrations associated with each projective $g$-module of $p$-character $\chi$, and finally obtain sum formulas from those filtrations.

Dong Liu (Huzhou Teachers College)

Title: Classification of Harish-Chandra modules over the Schr\"{o}dinger-Virasoro algebra.
Abstract: In this talk, we classify all irreducible weight modules with finite dimensional weight spaces over the Schrödinger-Virasoro algebra $\sv$. Meanwhile, all indecomposable modules with one dimensional weight spaces over the Schrödinger-Virasoro algebra $\sv$ are also determined.

Jinkui Wan (University of Virginia)

Title: Completely splittable representations of affine Hecke-Clifford algebras

Abstract: We classify and construct irreducible completely splittable representations of affine and finite Hecke-Clifford algebras over an algebraically closed field of characteristic not equal to $2$.

Yufeng Yao (East China Normal University)

Title: Support Varieties for Lie algebras of Cartan type
Abstract: In this presentation, we study support varieties for Lie algebras $L$ of Cartan type. We give some description for the support varieties of any finite dimensional $L$-module with character $\chi$, whenever the height of $\chi$ is not too big. Moreover, we can make a concrete computation for a class of modules with semisimple characters parallel to the arguments by Lin-Nakano on restricted modules and Shu on generalized restricted modules early.

Lei Zhao (University of Virginia)

Title: Modular representations of Lie superalgebras.
Abstract: Earlier, a superalgebra generalization of the Kac-Weisfeiler conjecture was formulated and established by Wang and the speaker for basic classical Lie superalgebras (which are the most important classes of Lie superalgebras) over characteristic p. We will present a new proof of this result by adapting the deformation arguments of Premet and Skryabin to reduced enveloping superalgebras. The new proof allows us to improve optimally the assumption on $p$ from our original proof. We will also establish a semisimplicity criterion using the technique of odd reflections for the reduced enveloping superalgebras associated with semisimple p-characters for all basic classical Lie superalgebras.

Lisun Zheng (Shanghai Institute of Technology)

Title: Cartan invariants in the category of restricted representation for general linear Lie superalgebras
Abstract: We compute the Cartan invariants for restricted representation of general linear Lie superalgebra by means of the restricted Kac module and restricted baby Verma module.

Abstracts of the Added Talks

Jinkui Wan （University of Virginia）

Title: Modular representations of wreath Hecke algebras and affine crystal basis
Abstract: We introduce a generalization of degenerate affine Hecke algebra, called wreath Hecke algebra, associated with an arbitrary finite group G. The simple modules of the wreath Hecke algebra and of its associated cyclotomic algebras are classified over an algebraically closed field of any characteristic p ≥ 0. The modular branching rules for these algebras are obtained, and when p does not divide the order of G, they are further identified with crystal graphs of integrable modules for quantum affine algebras. The key is to establish an equivalence between a module category of the (cyclotomic) wreath Hecke algebra and its suitable counterpart for the degenerate affine Hecke algebra.

Shizuo Zhang （Kansas State University）

Title: Noncommutative Grassmannian and quasi coherent sheaf.
Abstract: General theory of Noncommutative algebraic geometry was built by A.Rosenberg. I will give an introduction to this subject,in particular,some examples of noncommutative "space" such as noncommutative Grassmannian introduced by Kontsevich and Rosenberg(in particular,noncommutative projective space). I will also introduce the quasi coherent sheaf on "noncommutative space". If time allows, I will introduce the quantum D-scheme given by Lunts-Rosenberg and Tanisaki.