Eightieth BLOC meeting

BLOC

Bristol Leicester Oxford Colloquium

The eightieth meeting will be held on Wednesday 4th July 2018 in the Department of Mathematics, City, University of London. The talks are all in room ELG11.


 

Programme:

12.15 Lunch: Banana Tree, 412-416 St. John Street, London EC1V 4NJ

13.45 Gus Lehrer (Sydney) Invariant theory, classical, quantum and super

14.45 Emilie Dufresne (Nottingham) Separating invariants and local cohomology

Tea

16.30 Alex Malcolm (Bristol) Strong reality in finite simple groups: on products of classes and characters.

 


 

Abstracts

Gus Lehrer: I shall show how a geometric idea whose crux goes back to Atiyah may be applied to illuminate the fundamental theorems of invariant theory for classical reductive groups, their quantised enveloping algebras, and related super Lie algebras. This is joint work with R. Zhang, and some with P. Deligne, and illuminates the structure of certain algebras of endomorphisms.

Emilie DufresneThe study of separating invariants is a new trend in Invariant Theory and a return to its roots: invariants as a classification tool. For a finite group acting linearly on a vector space, a separating set is simply a set of invariants whose elements separate the orbits of the action. Such a set need not generate the ring of invariants. In this talk, we give lower bounds on the size of separating sets based on the geometry of the action. These results are obtained via the study of the local cohomology with support at an arrangement of linear subspaces naturally arising from the action. (Joint with Jack Jeffries.)

Alex MalcolmIn a finite simple group, the strongly real elements are those that are conjugate to their inverse by an involution. A related notion exists in the ordinary representation theory of the group, where we call an irreducible character orthogonal if it is not only real-valued, but has an underlying real representation. It was recently shown that any element of a finite simple group decomposes as a product of two strongly real elements, motivating the question as to whether an analogous result holds for irreducible characters? i.e. does every irreducible representation appear in the tensor product of two real reps? We will discuss the methods used in answering both of these questions, as they range from the analysis of finite simple group sub-structure, to a classical problem of computing Kronecker coefficients in the symmetric group.

 


 

Please let Joe Chuang know by July 2nd if you are coming to the meeting, especially if you are coming for lunch.

There will be time for informal discussions during the day.

 

The meeting is supported by an LMS Scheme 3 grant. This is used to help offset travel costs for those from institutions participating in the scheme, with priority given to speakers and postgraduates. Please note that, if travelling by train, then you should purchase an advance ticket where possible, since the grant will not cover standard open return tickets to London during peak hours.

Travel information is HERE.


For further information please contact one of the organisers:

Joe Chuang
Karin Erdmann
Jeremy Rickard
Nicole Snashall

 

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