Categorifying Turbulence in Borel Reducibility

Start date: 1 June 2021
End date: 31 May 2022
Funder: Engineering and Physical Sciences Research Council (EPSRC)
Value: £72,945
Partners and collaborators: Collaborator: Dr Filippo Calderoni, University of Illinois at Chicago
Primary investigator: Dr Andrew Brooke-Taylor

The framework of Borel reducibility allows us to compare the complexity of a variety of different mathematical problems. It has had much success in showing that certain classification programmes (in different areas of mathematics) were impossible tasks, using Hjorth's notion of turbulence as a central tool. However, the Borel reducibility framework has previously ignored an important feature of most classification programmes, known as functoriality.

The aim of this project is to find a functorial version of turbulence. In the longer term, this could be used to show that more classification programmes are impossible to complete.