The University of Leeds Algebra Seminar 2020/21  
Tuesdays 15:00 (currently online in zoom)  

Until further notice the seminar will take place online at 15:00 on Tuesdays. We will have virtual biscuits and tea (and coffee) before the seminar.

The Leeds Algebra Group .


October 6, 15:00 
Dixy Msapato  
(University of Leeds)  
Counting tau-exceptional sequences over Nakayama algebras  
October 13, 15:00 
Severin Bunk  
(Universität Hamburg)  
Universal Symmetries of Gerbes and Smooth Higher Group Extensions  
October 20, 15:00 
Ana Ros Camacho  
(Cardiff University)  
Algebraic structures in group-theoretical fusion categories  
October 27, 15:00 
David Jordan  
(University of Edinburgh)  
November 3, 15:00 
Tyler Kelly  
(University of Birmingham)  
Exceptional Collections in Mirror Symmetry  
November 10, 15:00 
Lutz Hille  
(Universität Münster)  
Moduli of quiver representations, quiver Grassmannians and morphisms  
November 17, 15:00 
Vincent Koppen  
(University of Leeds)  
On isotypic decompositions for non-semisimple Hopf algebras  
November 24, 15:00 
Xiuping Su  
(University of Bath)  
Auslander algebras of Nakayama algebras and (quantised) partial flag varieties  
December 1, 15:00 
David Jordan  
(University of Edinburgh)  
December 8, 15:00 
Tara Brendle  
(Unviersity of Glasgow)  
December 15, 15:00 


Dixy Msapato (University of Leeds): Counting tau-exceptional sequences over Nakayama algebras. The notion of a tau-exceptional sequence was introduced by Buan and Marsh in 2018 as a generalisation of exceptional sequences over finite dimensional algebras. In this talk, I will introduce both these notions, and present counting results of tau-exceptional sequences over some classes of Nakayama algebras. In some of these cases we will see obtain closed formulas counting other well known combinatorial objects, and exceptional sequences over some path algebras of Dynkin quivers.

Severin Bunk (Universität Hamburg): Universal Symmetries of Gerbes and Smooth Higher Group Extensions. Gerbes are geometric objects describing the third integer cohomology of a manifold and the B-field in string theory; they can essentially be understood as bundles of categories whose fibre is equivalent to the category of vector spaces. Starting from a hands-on example, I will explain gerbes and their categorical features. The main topic of this talk will then be the study of symmetries of gerbes in a universal manner. We will see that this is completely encoded in an extension of smooth 2-groups. If time permits, in the last part I will survey how this construction can be used to provide a new smooth model for the string group, via a theory of group extensions in $\infty$-topoi.

Ana Ros Camacho (Cardiff University): Algebraic structures in group-theoretical fusion categories. In a categorical sense, Morita equivalence is a useful notion (stemming from ring theory) that allows us to classify collections of objects. It has also nice applications in several topics in (mathematical) physics like e.g. rational conformal field theory. In this talk, we generalize results from Ostrik and Natale that describe Morita equivalence classes of certain algebra objects in pointed fusion categories to the case of group-theoretical fusion categories. These algebra objects also have very good properties that we will describe in detail. We will assume little knowledge of fusion categories. Joint work with the WINART2 team Y. Morales, M. Mueller, J. Plavnik, A. Tabiri and C. Walton..

Tyler Kelly (University of Birmingham): Exceptional Collections in Mirror Symmetry. I will give a few examples of where exceptional collections in categories arise in mirror symmetry and why they are useful. These are a (weaker) categorical version of tilting modules. I aim to focus on the homological algebra and will give a biased view, ending with a few results of D. Favero, D. Kaplan, and myself in this vein.

Lutz Hille (Universität Münster): Moduli of quiver representations, quiver grassmannians and morphisms. Moduli space of quiver representations have been introduced by King following Mumford's celebrated results on geometric invariant theory. So far, only a few moduli spaces are explicitly known. On the other side, quiver grassmannians became later of interest motivated by cluster algebras, however, also here only a few cases are understood. The key problem is the existence of sufficiently many morphisms between those spaces to start induction or to understand topological or K-theoretic properties.
A new idea developed in joint work with Blume produces sufficiently many morphisms, however not between the moduli spaces themself, but between their inverse limit. Similar techniques also work for quiver grassmannians.
The aim of this talk is to define the inverse limit, to give some easy examples and to show the advantage of this modified moduli space. At the end we discuss the geometry of this new spaces.

Vincent Koppen (University of Leeds): On isotypic decompositions for non-semisimple Hopf algebras. In this talk we consider the isotypic decomposition of the regular module of a finite-dimensional Hopf algebra over an algebraically closed field of characteristic zero. For a semisimple Hopf algebra, the idempotents realizing the isotypic decomposition can be explicitly expressed in terms of characters and the Haar integral. In this talk we investigate Hopf algebras with the Chevalley property, which are not necessarily semisimple. We find explicit expressions for idempotents in terms of Hopf-algebraic data, where the Haar integral is replaced by the regular character of the dual Hopf algebra. For a large class of Hopf algebras, these are shown to form a complete set of orthogonal idempotents. We give an example which illustrates that the Chevalley property is crucial.

Xiuping Su (University of Bath): Auslander algebras of Nakayama algebras and (quantised) partial flag varieties. Auslander algebras are quasi-hereditary algebras, which were introduced by L Scott to study highest weight categories in Lie theory. An important concept in this context is standard modules $\Delta_i$.
In this talk I will discuss certain subcategories of $\Delta-$filtered modules of some Auslander algebras and show that these are stably 2-CY categories. I will also explain how these categories lead to possible categorification of cluster algebras on the (quantised) coordinate rings of partial flag varieties. This talk is based on ongoing joint work with B T Jensen.

David Jordan (University of Edinburgh): TBA. TBA.

Tara Brendle (University of Glasgow): TBA. TBA.

For past algebra seminars see: 2019/20 , 2018/19 , 2017/18 .

This page is maintained by Eleonore Faber .