EPSRC : Jennifer Scoular : EP/L016826/1 A major hazard to engineering projects in London are geological features known as drift-filled hollows (DFHs). They are typically cone-shaped depressions in the bedrock filled with sand and gravel. DFHs can be up to 75 m deep and 90 to 475 m wide. They have been encountered on many small- and large-scale engineering projects in London, including the Thames Tideway Lee Tunnel, Crossrail, the Thames Water Ring Main and Battersea Power Station construction. These DFHs often contain water, therefore leading to water ingress whilst tunnelling as well as uneven settlement. The distribution of these features across London is poorly understood, due to their locations only being discovered during engineering projects. Engineers in London do not fully understand how these features formed. One hypothesis is that these features formed during historic glacial periods as pingos. Pingos are dome shaped mounds in cold regions characterised by permafrost. The dome shape is formed by an ice core, which is overlain with soil. The hypothesis is that, when these features melted in London, they were scoured out by rivers fed by glacial meltwater forming the DFHs we observe today. Regions where we can observe modern pingos is the Northwest Territories and Yukon territory of Canada. We propose both a fieldwork and remote sensing approach to test this hypothesis. Firstly, a direct inspection of pingo growth and characteristics of active pingos, followed by inspections of those that have collapsed. This will enable us to better understand if they could have formed in London in the past if the collapsed pingos in Canada share any characteristics with DFHs in London. Secondly, we will use remote sensing data including aerial photography, satellite imagery and digital elevation models, to make a digital map of the location of pingos in the Arctic. The locations may provide clues on factors that effect where they form, including water source for the ice and the type of soil they form under. From these observations, we aim to be able to conclude whether DFHs in London could have formed as pingos and if so, what factors affect their location to improve our knowledge of where to find them in London. With a major tunnelling project currently ongoing in London, the Thames Tideway Tunnel, also known as London's 'super-sewer', knowledge about the location of these hazardous features is of great importance.

EPSRC : Simon May : EP/R513258/1 This Globalink Research Placement should take place at Carleton University in the Autumn of 2020. It will allow the applicant Simon May to spend 12 weeks at the host university and complement the theoretical work in his Ph.D. thesis with explicit computations of matrix factorizations for discriminants of pseudo-reflection groups. It will also allow the applicant to take part in courses and research seminars at the host University in order to establish collaborations with the host supervisor and his group as well as to grow his professional network. The background for this work is the McKay correspondence, that relates three areas in pure mathematics: algebraic geometry, commuative algebra and representation theory of finite groups. Very recently, a McKay correspondence for reflection groups has been established, that relates irreducible representations of finite groups generated by reflections to certain modules over the coordinate rings of the discriminants of these reflection groups. These modules are maximal Cohen-Macaulay modules and can be described by so-called matrix factorizations. The goal of this project is to explicitly compute (in Macaulay2) matrix factorizations for discriminants of pseudo-reflection groups and so obtain insights that can lead to a better understanding of these objects.