Research
My research is based on the discretisation of spacetime to investigate quantum gravity effects. I have worked on fuzzy spaces, which are finite non-commutative geometries based upon matrix algebras. I am interested in how continuous symmetries affect these spaces. Outside non-commutative geometry, I am interested in exploring quantum geometries via numerical methods.
I am also interested in the development of quantum technologies, and the role of mathematics in the description of quantum phases of matter. For instance, there is a description of the quantum hall effect based upon the non-commutative torus. As a finite version has been developed, called the fuzzy torus, I am interested in investigating the consequence using this description would have for physics.
Publications
- PhD Thesis: Spectral Geometry of Fuzzy Spaces. Paul Druce: University of Nottingham (2020) PDF here
- Spectral estimators for finite non-commutative geometries. Barrett,J., Druce,P., Glaser, L.: J Phys Math Theor. 52, 275203 (2019). doi:10.1088/1751-8121/ab22f8
Google Scholar, INSPIRE-HEP, ORCID
Research notes and documents
- Introductory notes on category theory: Notes on Category Theory - in progress
- Notes on Geometric Quantisation: A footing in Geometric Quantisation
- Notes from a random seminar I went to in 2018. This was mainly to test my workflow for putting notes on the web.: Strong Quantum Energy Conditions and Hawking Singularity Theorems by Eleni Kontou (University of York)
- A report I made at the end of the second year of my PhD, summarising recent developments.: Second Year Report
- The slides from a talk given at Radboud University, Nijmegen in April 2017: Nijmegen Talk Slides
- A report made at the end of the first year of my PhD outlining the motivation and background of the project.: First Year Report
Notes for fun
- A poster I made for the conference Quantum Gravity on the Computer, here
- Revision guide made for Thermal Physics II for the University of Warwick Physics Society here
Research Blog Posts
- Introductory notes on category theory: Notes on Category Theory - in progress
- Notes on Geometric Quantisation: A footing in Geometric Quantisation
- Notes from a random seminar I went to in 2018. This was mainly to test my workflow for putting notes on the web.: Strong Quantum Energy Conditions and Hawking Singularity Theorems by Eleni Kontou (University of York)