Covariant Spectral Theory


Contact Dr Vladimir V. Kisil to discuss this project further informally.

Project description

Families of invertible transformations of geometric sets are rich sources of interesting and important groups. Properties of geometric objects, which are invariant under such transformations, are subject of geometry according to the Erlangen Programme of Felix Klein. Transformations of sets can be naturally extended to actions on linear functional spaces defined on those sets, so we obtain linear representations of groups.

There are many questions in analytic function theory which are greatly simplified by a consideration of an appropriate group representation. Finally, we can consider actions of the same groups on operators or, more generally, on Banach algebras and other non-commutative sets. There are oftenly intertwining operators linking group actions on non-commutative spaces and linear spaces of functions. Depending on the direction they act those intertwining operators are known as functional calculi or functional models.

A study of covariant properties of functional calculi provide valuable characterisation of operator spaces in geometrical terms. Thus it is a natural extension of the Erlangen programme to non-commutative sets.

Entry requirements

Applications are invited from candidates with or expecting a minimum of a UK upper second class honours degree (2:1), and/or a Master's degree in a relevant mathematics degree such as (but not limited to) pure mathematics.

How to apply

Formal applications for research degree study should be made online through the university's website. Please state clearly in the research information second that the PhD you wish to be considered for is 'Covariant Spectral Theory' as well as Dr Vladimir V. Kisil as your proposed supervisor.

If English is not your first language, you must provide evidence that you meet the University's minimum English Language requirements.

We welcome scholarship applications from all suitably-qualified candidates, but UK black and minority ethnic (BME) researchers are currently under-represented in our Postgraduate Research community, and we would therefore particularly encourage applications from UK BME candidates. All scholarships will be awarded on the basis of merit.