Project description

Motions capture the possible movements of a subset inside an ambient manifold. Motion groupoids, which are made up of equivalence classes of motions, are algebraic structures which appear to effectively model particle motion in certain condensed matter systems known as topological phases of matter. For example, considering points in 2-dimensional space leads to a realisation of the Artin braid groups.

Defect topological quantum field theories (TQFTs) also lead to models of topological phases of matter. Modelling spacetime using cobordisms, defect cobordisms are cobordisms together with lower dimensional regions, and attached labels. Defect TQFTs are then structure preserving maps assigning linear maps to evolutions of spacetime.

Motion groupoids and defect TQFTs are linked by their relationship to physics, but are distinct areas of mathematics. The aim of this project is to understand the mathematical relationship. The expectation is that bridging this gap will lead to new results on both sides.

Duration of stay: 1st April - 30th September 2023