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 events 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
9 October 201814:15to15:30Abstract regular polytopes and Y-shaped presentations for subgroups of the Monster sporadic simple groupDima PasechnikAbstract
Abstract regular polytopes are finite quotients of Coxeter complexes
with string diagram, satisfying a natural intersection property, see
e.g. [MMS2002]. They arise in a number of geometric and group-theoretic
contexts. The first class of such objects, beyond the
well-understood examples coming from finite and affine Coxeter groups,
are locally toroidal cases, e.g. extensions of quotients of the affine
F_4 complex [3,3,4,3]. In 1996 P.McMullen & E.Schulte constructed a
number of examples of locally toroidal abstract regular polytopes of
type [3,3,4,3,3], and conjectured completeness of their list. We
construct counterexamples to the conjecture using a Y-shaped
presentation for a subgroup of the Monster, and discuss various
- Algebra Seminar
- Representation Theory seminar
There are no seminars currently scheduled for this series.
An archive of previous events is also available.