14 November 2013

14:00

Lisa Lamberti

Abstract

In this talk I will introduce cluster categories and report on some new results on cluster categories of type E_6.

14 November 2013

14:00

Lisa Lamberti

Abstract

In this talk I will introduce cluster categories and report on some new results on cluster categories of type E_6.

5 November 2013

14:00

Chris Dodd

Abstract

<p>I will explain some ongoing work on understanding algebraic D-moldules
via their reduction to positive characteristic. I will define the p-cycle of
an algebraic D-module, explain the general results of Bitoun and Van
Den Bergh; and then discuss a new construction of a class of algebraic
D-modules with prescribed p-cycle.</p>

4 November 2013

14:00

to

16:00

31 October 2013

14:00

Lisa Lamberti

Abstract

In this talk I will give a definition of cluster algebra and state some main results.
Moreover, I will explain how the combinatorics of certain cluster algebras can be modeled in geometric terms.

24 October 2013

15:05

24 October 2013

14:00

18 October 2013

15:50

Andrzej Skowronski

Abstract

Let $A$ be a finite-dimensional $K$-algebra over an algebraically closed field $K$. Denote by $\Omega_A$ the syzygy operator on the category $\mod A$ of finite-dimensional right $A$-modules, which assigns to a module $M$ in $\mod A$ the kernel $\Omega_A(M)$ of a minimal projective cover $P_A(M) \to M$ of $M$ in $\mod A$. A module $M$ in $\mod A$ is said to be periodic if $\Omega_A^n(M) \cong M$ for some $n \geq 1$. Then $A$ is said to be a periodic algebra if $A$ is periodic in the module category $\mod A^e$ of the enveloping algebra $A^e = A^{\op} \otimes_K A$. The periodic algebras $A$ are self-injective and their module categories $\mod A$ are periodic (all modules in $\mod A$ without projective direct summands are periodic). The periodicity of an algebra $A$ is related with periodicity of its Hochschild cohomology algebra $HH^{*}(A)$ and is invariant under equivalences of the derived categories $D^b(\mod A)$ of bounded complexes over $\mod A$. One of the exciting open problems in the representation theory of self-injective algebras is to determine the Morita equivalence classes of periodic algebras.
We will present the current stage of the solution of this problem and exhibit prominent classes of periodic algebras.

18 October 2013

14:00

Radha Kessar

Abstract

We investigate symmetric quotient algebras of symmetric algebras,
with an emphasis on finite group algebras over a complete discrete
valuation ring R with residue field of positive characteristic p. Using elementary methods, we show that if an
ordinary irreducible character of a finite group gives
rise to a symmetric quotient over R which is not a matrix algebra,
then the decomposition numbers of the row labelled by the character are
all divisible by p. In a different direction, we show that if is P is a finite
p-group with a cyclic normal subgroup of index p, then every ordinary irreducible character of P gives rise to a
symmetric quotient of RP. This is joint work with Shigeo Koshitani and Markus Linckelmann.

18 October 2013

10:50

Vanessa Miemietz

Abstract

<p>We explain how Khovanov-Lauda-Rouquier algebras in finite
type A are affine cellular in the sense of Koenig and Xi. In particular
this reproves finiteness of their global dimension. This is joint work
with Alexander Kleshchev and Joseph Loubert.</p>

18 October 2013

09:30

Dave Benson

Abstract

This talk is about some recent joint work with Sarah Witherspoon. The representations of some finite dimensional Hopf algebras have curious behaviour: Nonprojective modules may have projective tensor powers, and the variety of a tensor product of modules may not be contained in the intersection of their varieties. I shall describe a family of examples of such Hopf algebras and their modules, and the classification of left, right, and two-sided ideals in their stable module categories.