[PDF] Quantum differential geometry and applications

76961_6Majid_2021.pdf 1

Quantum differential geometry and

applications

Supervisor: Shahn Majid

Research Group: Geometry & Analysis

Funding: For September 2021 entry: Funding may be available through QMUL Principal's Postgraduate Research Studentships, School of Mathematical Sciences Studentships, and EPSRC DTP, in competition with all other PhD applications. Studentships will cover tuition fees, and a stipend at standard rates for 3-3.5 years. We welcome applications for self-funded applicants year-round, for a January, April or

September start.

Project description:

Quantum differential geometry was developed in recent years as an extension to geometry to allow the `coordinate algebra' of a space to be noncommutative and/or for differential forms to not commute with coordinates. The theory includes Riemannian geometry as well as vector bundles with connection and works over any field. Having recently finished the textbook cited, the project will be particularly open to applications such as to quantum information and quantum geometry in ordinary quantum systems. Other directions could include models of quantum gravity over finite-dimensional algebras or could go in a theoretical direction where the calculus of variations, stress tensor and Einstein tensor remain poorly understood in quantum geometry.

References

E.J. Beggs and S. Majid, Quantum Riemannian Geometry, Grundlehren der mathematischen

Wissenschaften, Vol. 355, Springer (2020)

Further information:

How to apply

Entry requirements

Fees and funding

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