Dr Lewis Topley
Dr Lewis Topley, who joined the Department of Mathematical Sciences in June 2021, has brought with him a UK Research & Innovation Future Leaders Fellowship (UKRI FLF). Dr Topley's FLF project explores "Geometric Representation Theory and W-algebras" and runs until February 2024, with a possible 3-year extension.
When asked about his research, Dr Topley said, "The project aims to develop the theory of W-algebras, which are a relatively new tool in representation theory that are becoming more and more important. They first arose in mathematical physics in the context of two dimensional conformal field theory, and have now become one of the key tools in representation theory, where they provide a rich, complex picture, feeding into many classical problems in the field."
Although W-algebras are reasonably well-understood over the complex numbers, understanding their structure and representation theory over fields of positive characteristics has remained shrouded in mystery, and is only now beginning to unravel. One of Dr Topley's current objectives is to work out the correct definition of an affine W-algebra in the modular setting and develop the relationship with their finite counterparts. In the coming months Dr Topley will be advertising a 3-year postdoc position to support his research.
UKRI Future Leaders Fellowships are awarded to support talented people in universities and other innovative environments, who can apply for up to £1.5 million over four years to support their research and develop their careers.
Dr Matt Roberts
A 3-year extension of his Royal Society University Research Fellowship has been awarded to Dr Matt Roberts, a Reader in probability, Co-Director of Prob-L@B and Chair of the Department Equality and Diversity Committee.
Dr Roberts has been a Royal Society University Research Fellow since 2016, working on spatial dependence in branching structures, including applications to random graphs. His fellowship was recently extended to study detailed sample path asymptotics for random walks and Brownian motion, with the aim of gaining further insight into spatially-dependent branching structures and perhaps even branching processes with interactions.