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, 21/05 17:00	Anreas Doering (Oxford)	Algebra Seminar	L2
	Spectral presheaves as generalised (Gelfand) spectra
	The spectral presheaf of a nonabelian von Neumann algebra or C*-algebra was introduced as a generalised phase space for a quantum system in the so-called topos approach to quantum theory. Here, it will be shown that the spectral presheaf has many features of a spectrum of a noncommutative operator algebra (and that it can be defined for other classes of algebras as well). The main idea is that the spectrum of a nonabelian algebra may not be a set, but a presheaf or sheaf over the base category of abelian subalgebras. In general, the spectral presheaf has no points, i.e., no global sections. I will show that there is a contravariant functor from unital C*-algebras to their spectral presheaves, and that a C*-algebra is determined up to Jordan *-isomorphisms by its spectral presheaf in many cases. Moreover, time evolution of a quantum system can be described in terms of flows on the spectral presheaf, and commutators show up in a natural way. I will indicate how combining the Jordan and Lie algebra structures may lead to a full reconstruction of nonabelian C*- or von Neumann algebra from its spectral presheaf.

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

Representation Theory seminar

Tue, 21/05 14:00	Kevin McGerty (Oxford)	Representation Theory Seminar	L2
	Introduction to deformation quantisations in algebraic geometry

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

Kinderseminar

Wed, 22/05 11:30	Levon Haykazyan	Algebra Kinderseminar	Queen's College
	To Be Announced

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.