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, 16/02 17:00	John Duncan (Cambridge)	Algebra Seminar	L2
	Monstrous moonshine and black holes
	In 1939 Rademacher derived a conditionally convergent series expression for the modular j-invariant, and used this expression—the first Rademacher sum—to verify its modular invariance. We may attach Rademacher sums to other discrete groups of isometries of the hyperbolic plane, and we may ask how the automorphy of the resulting functions reflects the geometry of the group in question.    In the case of a group that defines a genus zero quotient of the hyperbolic plane the relationship is particularly striking. On the other hand, of the common features of the groups that arise in monstrous moonshine, the genus zero property is perhaps the most elusive. We will illustrate how Rademacher sums elucidate this phenomena by using them to formulate a characterization of the discrete groups of monstrous moonshine.   A physical interpretation of the Rademacher sums comes into view when we consider black holes in the context of three dimensional quantum gravity. This observation, together with the application of Rademacher sums to moonshine, amounts to a new connection between moonshine, number theory and physics, and furnishes applications in all three fields.

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

Representation Theory seminar

Thu, 11/02 14:30	Mary Schaps (Bar Ilan, Israel)	Representation Theory Seminar	L3
	Generating the crystal graph for cyclotomic Hecke algebras

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

Kinderseminar

11:30		Algebra Kinderseminar
	NO SEMINAR

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

An archive of previous events is also available.