Algebra Research Group

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, 05/06 17:00	Professor S. Rees (Newcastle)	Algebra Seminar	L2
	Artin groups of large type: from geodesics to Baum-Connes
	I’ll report on my recent work (with co-authors Holt and Ciobanu) on Artin groups of large type, that is groups with presentations of the form G = hx1, . . . , xn | xixjxi · · · = xjxixj · · · , 8i < ji for which both sides of the ‘braid relation’ on xi and xj have length mij 2 N [1 with mij  3. (In fact, our results still hold when some, but not all possible, relations with mij = 2 are allowed.) Recently, Holt and I characterised the geodesic words in these groups, and described an effective method to reduce any word to geodesic form. That proves the groups shortlex automatic and gives an effective (at worst quadratic) solution to the word problem. Using this characterisation of geodesics, Holt, Ciobanu and I can derive the rapid decay property for most large type groups, and hence deduce for most of these that the Baum-Connes conjec- ture holds; this has various consequence, in particular that the Kadison- Kaplansky conjecture holds for these groups, i.e. that the group ring CG contains no non-trivial idempotents. 1

For any corrections/updates to these listings, please contact seminars [-at-] maths [dot] ox [dot] ac [dot] uk.

Representation Theory seminar

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Kinderseminar

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An archive of previous events is also available.