Numerical simulation of random Dirac operators
Lead Research Organisation:
University of Nottingham
Department Name: Sch of Mathematical Sciences
Abstract
A Riemannian manifold can be described without loss of information by a spectral triple (A,H,D), where H is a Hilbert space, A is a (commutative) algebra with a representation in H and D is a Dirac operator acting on H. The spectral triple, however, also allows for an extension of the notion of geometry: by considering a spectral triple with a non-commutative algebra, one obtains a so-called non-commutative geometry.
A class of non-commutative geometries known as fuzzy spaces is introduced, and their behaviour when the Dirac operator is allowed to fluctuate according to a certain probability measure is investigated by means of Markov chain Monte Carlo integration.
A class of non-commutative geometries known as fuzzy spaces is introduced, and their behaviour when the Dirac operator is allowed to fluctuate according to a certain probability measure is investigated by means of Markov chain Monte Carlo integration.
Organisations
People |
ORCID iD |
John Barrett (Primary Supervisor) | |
Mauro D'Arcangelo (Student) |
Studentship Projects
Project Reference | Relationship | Related To | Start | End | Student Name |
---|---|---|---|---|---|
EP/N50970X/1 | 01/10/2016 | 30/09/2021 | |||
1947394 | Studentship | EP/N50970X/1 | 01/10/2017 | 30/09/2020 | Mauro D'Arcangelo |