Spring 2018
In Spring Term 2018, the LAC will be held at City University (room ELG08), organized by Joseph Chuang and Jorge Vitória. The talks begin at 17.00, with tea being served in the common room at 16.30.
18th January  Simon Peacock (Bristol)  Representation dimension and separable equivalences 
25th January  Ivan Tomašić (Queen Mary)  Cohomology of difference algebraic groups 
1st February  Joseph Karmazyn (Sheffield)  Equivalences of singularity categories via noncommutative algebras 
8th February  Eugenio Giannelli (Cambridge)  TBA 
15th February  Ivo Dell’Ambrogio (Lille)  TBA 
22nd February  Sira Gratz (Glasgow)  TBA 
1st March  Greg Stevenson (Glasgow)  TBA 
15th March  Nadia Mazza (Lancaster)  TBA 
22nd March  David Pauksztello (Lancaster)  TBA 
29th March  Wajid Mannan (Queen Mary)  TBA 
Abstracts
Simon Peacock (Bristol)
Representation dimension and separable equivalences
The representation dimension of an algebra is a finite integer that is supposed to indicate how complicated an algebra’s module category is. This dimension was first introduce by Auslander in 1971 and is, in general, notoriously hard to compute. This measure is related to the representation type of an algebra: an algebra has finite representation type if and only if it’s representation dimension is less than 3.
Separable equivalence is an equivalence relation on finite dimensional algebras. Over a field of a characteristic p, a group algebra is separably equivalent to the group algebra of its Sylow psubgroup. We use this relationship between a group and its Sylows to put an upper bound on the representation dimension of a group algebra for any finite group with a elementaryabelian Sylow subgroup.
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Ivan Tomašić (Queen Mary)
Cohomology of difference algebraic groups
Difference algebra studies algebraic structures equipped with an endomorphism/difference operator, and difference algebraic varieties are defined by systems of difference polynomial equations over difference rings and fields. In this talk, we will:
— argue that twisted groups of Lie type are best viewed as difference algebraic groups;
— develop the cohomology theory of difference algebraic groups;
— compute the cohomology in a number of interesting cases, and discuss its applications.
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Joseph Karmazyn (Sheffield)
Equivalences of singularity categories via noncommutative algebras
Singularity categories are triangulated categories occurring as invariants associated to singular algebras. For hypersurface singularities these categories can be realised via matrix factorisations, and in this case Knorrer periodicity constructs equivalences between the singularity categories of many different hypersurfaces.
I will discuss these ideas, and talk about how equivalences of singularity categories in the nonhypersurface (and nonGorenstein) setting can be constructed by considering quasihereditary noncommutative resolutions produced from certain geometric situations. In addition, Ringel duality has a very explicit description and interpretation for these quasihereditary algebras.
Previous seminars
Autumn 2017
The Autumn 2017 seminars will be held at Imperial College on Thursdays throughout the term, and will begin at 5pm unless otherwise stated. The room will be Huxley 130 unless otherwise stated. Organizer: John Britnell
October 12  Chris Bowman (Kent)  Complex reflection groups of type G(l,1,n) and their deformations  
October 19  John MacQuarrie (UFMG)  The path algebra as a left adjoint functor  
October 26  Alexander Molev (Sydney)  Vinberg’s problem for classical Lie algebras  
November 2  no colloquium  
November 9  Joanna Fawcett (Imperial)  Partial linear spaces with symmetry  
November 16  Dan Segal (Oxford)  Small profinite groups  
November 23  Jason Semeraro (Leicester)  Representations of Fusion Systems  
November 30  Emilio Pierro (LSE)  Finite simple quotients of Mapping Class Groups  
December 7 Double  3.30pm Charlotte Kestner (Imperial)  Strongly Minimal Semigroups  
5.00pm Dugald MacPherson (Leeds)  Model theory of profinite groups  
December 14  Florian Eisele (City)  A counterexample to the first Zassenhaus conjecture 
Summer 2017
In Summer Term 2017, the LAC was held at City University, organized by Jorge Vittoria.
8th June (ELG04 City University)  Jay Taylor (Arizona)  HarishChandra Induction and Lusztig’s Jordan Decomposition of Characters 
22nd June (ELG04 City University)  Arik Wilbert (Bonn)  Twoblock Springer fibers and Springer representations in type D 
29th June (ELG08 City University)  Benjamin Briggs (Bonn)  The characteristic action of Hochschild cohomology, and Koszul duality 
4th July (ELG08 City University)  Andrew Mathas (Sydney)  Jantzen filtrations and graded Specht modules 
20th July (ELG08 City University)  Olaf Schnürer (Bonn)  Geometric applications of conservative descent for semiorthogonal decompositions 
Abstracts:
Title: Geometric applications of conservative descent for semiorthogonal decompositions
Motivated by the local flavor of several wellknown semiorthogonal decompositions in algebraic geometry we introduce a technique called “conservative descent” in order to establish such decompositions locally. The decompositions we have in mind are those for projective bundles, blowups and root constructions. Our technique simplifies the proof of these decompositions and establishes them in greater generality. We also discuss semiorthogonal decompositions for BrauerSeveri varieties.
This is joint work with Daniel Bergh (Copenhagen).
Title: Jantzen filtrations and graded Specht modules
The Jantzen sum formula is a classical result in the representation theory of the symmetric and general linear groups that describes a natural filtration of the modular reductions of the simple modules of these groups. Analogues of this result exist for many algebras including the cyclotomic Hecke algebras of type A. Quite remarkably, the cyclotomic Hecke algebras of type A are now know to admit a Zgrading because they are isomorphic to cyclotomic KLR algebras. I will explain how to give an easy proof of the Jantzen sum formula for the Specht modules of the cyclotomic Hecke algebras of type A using the KLR grading. I will discuss some consequences and applications of this approach.
Title: Twoblock Springer fibers and Springer representations in type D
Abstract: We explain how to construct an explicit topological model for
every twoblock Springer fiber of type D. These socalled topological
Springer fibers are homeomorphic to their corresponding algebrogeometric
Springer fiber. They are defined combinatorially using cup diagrams which
appear in the context of finding closed formulas for parabolic
KazhdanLusztig polynomials of type D with respect to a maximal parabolic
of type A. As an application it is discussed how the topological Springer
fibers can be used to reconstruct the famous Springer representation in an
elementary and combinatorial way.
Spring 2017
In Winter/Spring 2017 the LAC was hosted at Queen Mary, University of London, organized by John Bray. The seminars will usually begin at 4:45pm (the traditional LAC start time). They all take place in the Fogg Lecture Theatre, Fogg Building (SBCS).
19 January (5pm)  Alex Fink (Queen Mary)  Characteristic polynomials from reciprocal planes in two ways 
26 January  Ben Fairbairn (Birkbeck)  A Baby, Some Bathwater & What I Did on my Holidays 
2 February  Behrang Noohi (Queen Mary)  Explicit HRStilting 
9 February  Rieuwert J. Blok (Bowling Green State University, Ohio, visiting Birmingham (UK))  CANCELLED, owing to illness. 
16 February  Chimere S. Anabanti (Birkbeck)  Three questions of Bertram on locally maximal sumfree sets. 
23 February  Rieuwert J. Blok (Bowling Green State University, Ohio, visiting Birmingham (UK))  3spherical Curtis–Tits groups 
2 March  Michael Wibmer (University of Pennsylvania)  Differential Embedding Problems over Complex Function Fields 
16 March  Susama Agarwala (US Naval Academy)  Mixed Tate Motives from Graphs 
23 March  Ben Smith (QMUL)  An Algebraic Approach to Generalised Frobenius Numbers 
30 March  Alla Detinko (St Andrews)  TBA 
In Autumn 2016 the LAC was hosted at City University, organized by Chris BowmanScargill. The seminars began at 5pm. Room details will be added to the list of seminars below shortly.
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6 October ELG08  Michael Bate (York)  Geometric Invariant Theory without Etale Slices 
13 October EM01  Lewis Topley (Bristol)  Modular finite Walgebras and their applications 
20 October EM01  Jan Grabowski (Lancaster)  Recovering automorphisms of quantum spaces 
27 October EM01  Robert Marsh (Leeds)  Dimer models and cluster categories of Grassmannians 
3 November EM01  Jorge Vitoria (City)  Silting modules and ring epimorphisms 
10 November EM01  Florian Eisele (City)  Tame blocks 
17 November EM01  Neil Saunders (City) 
On the Exotic Springer Correspondence

24 November EM01  Kevin McGerty (Oxford)  Kirwan surjectivity for quiver varieties 
1 December ELG08  Mark Wildon (Royal Holloway)  Plethysms: permutations, weights and Schur functions 
8 December ELG08  Tim Burness (Bristol)  Generating simple groups and their subgroups 