School of Mathematics and Physics

Location:  Lincoln
Salary:   From £34,304 pro rata
Please note, this post is full time at 1.0 FTE and fixed term for 36 months
Closing Date:   Wednesday 06 October 2021
Interview Date:   To be confirmed
Reference:  COS839

We are seeking a Postdoctoral Research Associate with a background in permutation groups or locally compact groups, to work alongside Associate Professor Simon M Smith at the Charlotte Scott Research Centre for Algebra, part of the School of Mathematics and Physics at the University of Lincoln. The post-holder will be supported by a grant from the EPSRC.

The successful candidate will work with Simon on an exciting EPSRC-funded project exploiting the interplay between locally compact groups and permutation groups. The study of locally compact groups famously breaks into two cases: the connected case and the totally disconnected case. The solution of Hilbert's Fifth problem led to a broad understanding of the connected case. Understanding the totally disconnected case (henceforth, tdlc) is now a central problem in group theory. We now know compactly generated tdlc groups are strongly related to permutation groups and that they can be "decomposed" into "simple pieces". A central focus of tdlc theory is to understand these "simple pieces", since they hold the key to understanding the structure of all compactly generated tdlc groups. It is known (via a permutational construction called the "box product") that we cannot understand these "simple pieces" using the isomorphism relation. However, it is thought that they might be understood using the "local isomorphism" relation, where two groups are locally isomorphic if they have isomorphic "local" (i.e. compact open) subgroups. This EPSRC-funded project seeks to better understand the local isomorphism relation, by studying it in the context of permutation groups where it can be defined in terms of certain isomorphisms between stabilisers of finite sets.

Applicants will be expected to have (or be close to finishing) a PhD in mathematics. It is not expected that applicants are familiar with all aspects of the project. However, they should possess sufficient specialist knowledge in one of the following:

• Permutation groups (preferably infinite)
• Locally compact groups
• Groups acting as automorphisms of infinite combinatorial or geometric structures (for example trees, graphs, hypergraphs, relational structures, buildings, etc)

Applicants should have excellent communication skills, including the ability to write for publications and give research talks. Successful candidates will be expected to play an active role in the Charlotte Scott Research Centre for Algebra at the University of Lincoln.

We are particularly keen to encourage applications from underrepresented groups in STEM.

For informal enquiries please contact Associate Professor Simon M Smith (sismith@lincoln.ac.uk).