Operator algebras attached to semigroups

The School of Mathematical Sciences of Queen Mary University of London invite applications for a PhD project commencing either in September 2016 (funded students) or at any point in the academic year (self-funded students).
Operator algebras form an interesting and active area of mathematical research, which is connected to various mathematical disciplines like functional analysis, topology, geometry, representation theory or dynamical systems, to mention just a few.

The main goal of this project is to study a particular class of C*-algebras, namely semigroup C*-algebras, and to explore the connection to group theory or semigroup theory. The idea is to focus on C*-algebras attached to semi- groups which naturally arise in group theory, for instance Artin monoids, like Braid monoids, or Baumslag-Solitar monoids, or the Thompson monoid. Another class of examples which have come up recently are semigroups of number-theoretic origin. Apart from C*-algebras, non-self adjoint operator algebras attached to semi-groups are also interesting and worth studying. They have not been studied as intensively as their C*-algebraic counterparts. It is reasonable to expect that they will exhibit fascinating new phenomena.

There are many interesting open questions related to the examples mentioned above, for instance, questions about general Artin groups or the Thompson group. It would be very interesting to reformulate or even try to attack these questions using operator algebras attached to semigroups. And since there are strong connections to dynamical systems and number theory, this project really has a highly interdisciplinary character. Last but not least, this area of research is of current interest and has seen some remarkable progress recently.

This project will be supervised by Dr Xin Li.

For full details, please see the project abstract: http://www.maths.qmul.ac.uk/sites/default/files/phd%20projects%202015/G&A/li.pdf

The application procedure is described on the School website. For further enquiries please contact Dr. Xin Li ([Email Address Removed]).

This project is eligible for several sources of full funding for the 2016/17 academic year, including support for 3.5 years’ study, additional funds for conference and research visits and funding for relevant IT needs. Applicants interested in the full funding will have to participate in a highly competitive selection process. The best candidates will be eligible to receive a prestigious Ian Macdonald Postgraduate Award of £1000, for which you will be considered alongside your application. The application deadline for full funding is January 31st 2016.

There is also 50% funding scheme available for students who are able to find the matching 50 % of the cost of their studies. Competition for these half-funded slots will be less intensive, and eligible students should mention their willingness to be considered for them in their application. The application deadline for 50 % funding is January 31st 2016.

This project can be also undertaken as a self-funded project, either through your own funds or through a body external to Queen Mary University of London. Self-funded applications are accepted year-round.