# Young Women in Representation Theory

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Schedule

 Thursday Friday Saturday 8.45 - 9.15 Registration 9.15 - 10.15 Lecture Idun Reiten Lecture Vanessa Miemietz Lecture Idun Reiten 10.15 - 10.45 Coffee Coffee Coffee 10.45 - 11.15 Talk Magdalena Boos Talk Tânia Silva Talk Lara Bossinger 11.30 - 12.00 Talk Rosanna Laking Talk Asilata Baptat Talk Sira Gratz 12.00 - 13.30 Lunch Lunch Snacks 13.30 - 14.30 Lecture Vanessa Miemietz Lecture Idun Reiten 14.30 - 17.00 Poster Coffee Poster Coffee 17.00 - 17.30 Talk Hannah Keese Talk Viviana Gubitosi 17.45 - 18.15 Talk Emily Norton 19.00 - Dinner

Lecture series

Idun Reiten will give a lecture series on tilting theory and Vanessa Miemietz will give a lecture series on Hecke algebras and categorification.

List of talk abstracts

Magdalena Boos,
Title: A finiteness criterion for parabolic conjugation,
Abstract: Let P be a parabolic upper-block subgroup of GLn(C). We look at the conjugation-action of P on the variety of nilpotent matrices in Lie(P). Our main question is motivated by the study of commuting varieties and reads as follows: "Does the mentioned P-action only admit a finite number of orbits?" We answer this question by developing a complete classification of finite actions. The proof makes use of methods from Representation Theory of finite-dimensional algebras and we sketch the main ideas and techniques. (Joint work with M. Bulois)

Rosanna Laking,
Title: The Krull-Gabriel dimension of a category,
Abstract: In this talk we will consider categories of finitely presented functors from a module category to the category of abelian groups.  Such categories turn out to be a natural setting in which we may study the morphisms between finitely presented modules and the Krull-Gabriel dimension can be seen as a measure of the complexity of the morphism structure in the module category.  It is calculated via iterated localisation of the functor category and we will give lots of examples in the context of finite-dimensional algebras in order to demonstrate how the Krull-Gabriel dimension effectively reflects the structure of the module category.  In particular I will report on joint work with K. Arnesen, D. Pauksztello, and M. Prest as well as joint work with M. Prest and G. Puninski.

Hannah Keese,
Title: A current algebra action on annular Khovanov homology,
Abstract: A well-known example of categorification is Khovanov homology, a homological invariant of knots and links that categorifies the Jones polynomial. Constructions such as this one introduce algebraic structure that can be very interesting from the perspective of representation theory. We will consider a modified Khovanov invariant, first introduced by Asaeda, Przytycki and Sikora, by restricting knots and links to a thickened annulus in $\mathbb{R}^3$ and equipping the resulting chain complex with a Lie algebra action. The homology theory that this produces is an annular link invariant that not only tracks the usual $q$-grading of regular Khovanov homology but also has the structure of a truncated current algebra module. We will discuss the construction of annular Khovanov homology and the representation theory of the associated current algebra. This is based on work by Grigsby, Licata and Wehrli.

Tânia Silva,
Title: Two different approaches to the representation theory of the symmetric group and the rook monoid,
Abstract: There's a long history about the representation theory of the symmetric group and the rook monoid. Since the 19th century many mathematicians contributed to this theories, where the Young diagrams always take an important role. We'll try to resume the classic approach, which uses the Young symmetrizers and the Specht modules, and a more recent one which uses Jucys-Murphy elements and Gelfand-Zetlin bases.

Asilata Bapat,
Title: GIT compactifications of Calogero-Moser spaces,
Abstract: The Calogero-Moser space is a symplectic algebraic variety that deforms the Hilbert scheme of points on a plane. It can be interpreted in many ways, for example as the parameter space of irreducible representations of a Cherednik algebra, or as a Nakajima quiver variety. It has a partial compactification that can be described combinatorially using Schubert cells in a Grassmannian. The aim of my talk is to introduce the Calogero-Moser space, and to describe some work in progress towards constructing another partial compactification using Geometric Invariant Theory (GIT).

Viviana Gubitosi,
Title: Derived class of $m$-cluster tilted algebras of type A tilde,
Abstract: In this talk we characterize all the finite dimensional algebras that are derived equivalent to an $m$−cluster tilted algebras of type A tilde.

Emily Norton,
Title: BGG resolutions for Cherednik algebras,
Abstract: The existence of closed character formulas for certain simple modules in Category $O$ of a Cherednik algebra motivated us to look for resolutions of these simple modules by standard modules ("BGG resolutions"). We prove a general criterion for when every simple module in a block of a highest weight category has a BGG resolution. Then we identify a class of examples satisfying our criterion in the Categories $O$ of rational Cherednik algebras of cyclotomic type. This is joint work with Stephen Griffeth.

Lara Bossinger,
Title: Toric degenerations in representation theory and beyond,
Abstract: Toric degenerations can be applied to different objects with representation theoretic relevance such as Schubert varieties, flag varieties and Grassmannains using a variety of approaches from combinatorics, Lie theory and cluster theory. As an example I will give a classification of the toric degenerations for Gr(2,n) using combinatoric methods and explain a translation into cluster theory. This is particularly interesting as it connects further to mirror symmetry and cluster duality.

Sira Gratz,
Title: Torsion pairs in discrete cluster categories of Dynkin type A,
Abstract: Igusa and Todorov introduced discrete cluster categories of Dynkin type A, which generally are of infinite rank. That is, their clusters contain infinitely many pairwise non-isomorphic indecomposable objects. In joint work with Holm and Joergensen we study torsion pairs in these categories and provide a combinatorial classification. Cluster tilting subcategories, t-structures, and co t-structures are all particular instances of torsion pairs and from our classification we are able to describe each of these classes. In particular, there are no non-trivial co t-structures but, contrary to the finite case, there are a number of interesting t-structures.

Last update: 19.07.2016