This term’s seminars

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 p-subgroup. 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 elementary-abelian 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 non-hypersurface (and non-Gorenstein) setting can be constructed by considering quasi-hereditary noncommutative resolutions produced from certain geometric situations. In addition, Ringel duality has a very explicit description and interpretation for these quasi-hereditary 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) Harish-Chandra Induction and Lusztig’s Jordan Decomposition of Characters
22nd June (ELG04 City University) Arik Wilbert (Bonn) Two-block 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 semi-orthogonal decompositions

Abstracts:

Title: Geometric applications of conservative descent for semi-orthogonal decompositions

Motivated by the local flavor of several well-known semi-orthogonal 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, blow-ups and root constructions. Our technique simplifies the proof of these decompositions and establishes them in greater generality. We also discuss semi-orthogonal decompositions for Brauer-Severi 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 Z-grading 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: Two-block Springer fibers and Springer representations in type D

Abstract: We explain how to construct an explicit topological model for
every two-block Springer fiber of type D. These so-called topological
Springer fibers are homeomorphic to their corresponding algebro-geometric
Springer fiber. They are defined combinatorially using cup diagrams which
appear in the context of finding closed formulas for parabolic
Kazhdan-Lusztig 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 HRS-tilting
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 sum-free sets.
23 February Rieuwert J. Blok (Bowling Green State University, Ohio, visiting Birmingham (UK)) 3-spherical 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 Bowman-Scargill. 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 W-algebras 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
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