Welcome to the pages of the Algebra group in the Mathematical Institute at Oxford. Here you will find information on our members, the seminars and other regular events and conferences we organise, news about us and the research networks we participate in. There are also lists of lecture courses related to our interests.
The research interests of the group span group theory, representation theory and algebraic aspects of geometry, among many other topics. For more detailed information on the people in our group and their individual research interests, please see our list of members.
If you are interested in undertaking graduate studies with us, please see the department's information for prospective graduate students. Post-doctoral positions and funding opportunities and faculty positions are listed on the Institute's vacancies page.
Details of the next scheduled seminar in each of the series we organise are listed below. For future events, please follow the link to each seminar's listings.
- Algebra seminar
-
Tue, 24/11
17:00Tim Burness (Southampton) Algebra Seminar L2 Let G be a permutation group on a set S. A base for G is a subset B of S such that the pointwise stabilizer of B in G is trivial. We write b(G) for the minimal size of a base for G.
Bases for finite permutation groups have been studied since the early days of group theory in the nineteenth century. More recently, strong bounds on b(G) have been obtained in the case where G is a finite simple group, culminating in the recent proof, using probabilistic methods, of a conjecture of Cameron.
In this talk, I will report on some recent joint work with Bob Guralnick and Jan Saxl on base sizes for algebraic groups. Let G be a simple algebraic group over an algebraically closed field and let S = G/H be a transitive G-variety, where H is a maximal closed subgroup of G. Our goal is to determine b(G) exactly, and to obtain similar results for some additional base-related measures which arise naturally in the algebraic group context. I will explain the key ideas and present some of the results we have obtained thus far. I will also describe some connections with the corresponding finite groups of Lie type.
- Representation Theory seminar
-
Thu, 26/11
14:30Anne Shepler (Denton, Texas and RWTH, Aachen) Representation Theory Seminar L3 Hochschild cohomology governs deformations of algebras, and its graded Lie structure plays a critical role. We explore this structure for a finite group G acting on an algebra S by automorphisms. We capture the group together with its action with the natural semi-direct product, S#G, known as the "skew group algebra" or "smash product algebra". For example, when G acts linearly on a complex vector space V, it induces an action on the symmetric algebra S(V), a polynomial ring. The semi-direct product S(V)#G is a surrogate for the ring of invariant polynomials on V; it serves as the coordinate ring for the orbifold arising from the action of G on V. Deformations of this skew group algebra S(V)#G play a prominent role in representation theory. Such deformations include graded Hecke algebras (originally defined independently by Drinfeld and by Lusztig), symplectic reflection algebras (investigated by Etingof and Ginzburg in the study of orbifolds), and rational Cherednik algebras (introduced to solve Macdonald's inner product conjectures). We explore the graded Lie structure (or Gerstenhaber bracket) of the Hochschild cohomology of skew group algebras with an eye toward deformation theory. For abelian groups acting linearly, this structure can be described in terms of inner products of group characters. (Joint work with Sarah Witherspoon.)
- Kinderseminar
-
Wed, 25/11
11:30Algebra Kinderseminar
An archive of previous events is also available.
This page is maintained by Jan E. Grabowski. Please use the contact form for feedback and comments.
