Address: |
School of Mathematical Sciences,Queen Mary University of London,Mile End Road, London E1 4NS |

Office: |
W317 |

Email: |
liam.williams@qmul.ac.uk |

I am a postgraduate research student in the Geometry & Analysis group at the School of Mathematical Sciences at Queen Mary, University of London. I am also a member of the Quantum Algebra group along with my supervisor Prof. Shahn Majid.

My research interests relate to the field of noncommutative geometry and quantum groups, in particular the role of quantum Riemannian geometry as an effective theory for quantum gravity effects. I am investigating the semiclassicalisation of the theory in the form of Poisson-Riemannian geometry as well as a new reconstructive approach using central extensions of differential graded algebras.

- S. Majid & L. Williams, Quantum Koszul formula on quantum spacetime, J. Geom. Phys., 129 (2018), pp.41-69
- S. Majid & L. Williams, Poisson principal bundles, in preparation...

- The Ann Cook Prize 2017

- "Quantum Koszul formula on quantum spacetime, Bayrischzell Workshop, Germany 2018
- "Quantum differential calculus", Royal Institute Masterclass, QMUL 2018
- "The theory of special relativity", City Academy Hackney, London 2018
- "On the origin of time", Queen Mary Internal Postgraduate Seminar, QMUL 2017
- "Quantum Koszul formula on quantum spacetime", ALSPAG conference, Queen's University Belfast 2017
- "Poisson Riemannian geometry and semiquantisation", London Junior Geometry Seminar, UCL 2017
- "Central extensions of differential graded algebras", Queen Mary Internal Postgraduate Seminar, QMUL 2016
- "Courant algebroids and Poisson-Riemannian geometry", Quantum Algebra Seminar, QMUL 2016
- "Introduction to noncommutative geometry, Queen Mary Internal Postgraduate Seminar, QMUL 2016

- Progress and Visions in Quantum Theory in View of Gravity, Max Planck Institute, Leipzig 2018
- Bayrischzell Workshop, On Noncommutativity and Physics: Hopf algebras in Noncommutative Geometry, Bayrischzell 2018
- ALSPAG: Non-commutative and nonassociative algebraic structures in geometry and physics, Queen's University, Belfast 2017
- Andrew Wiles, Oxford Mathematics London Public Lecture, London 2017
- Quantum Gravity in Paris, Institut Henri Poincaré, Paris 2017
- London Geometry and Topology Seminar, Imperial College London, London 2016
- Higher Structures in String Theory and Quantum Field Theory, Erwin Schrödinger Institute, Vienna 2015
- Einstein's legacy: celebrating 100 years of general relativity, QMUL, London 2015

**2019**

- Teaching associate, demonstrator and marker for undergraduate course: Introduction to Differential Geometry (MTH5113), QMUL

**2018**

- Co-supervised masters level student. Thesis title: "Marginally Stable Circular Orbits for Higher Dimensional Black Holes"
- Teaching associate and demonstrator for undergraduate course: Algebraic Structures I (MTH5100), QMUL
- Demonstrator and marker for undergraduate course: Partial Differential Equations (MTH6151), QMUL

**2017**

- Demonstrator for undergraduate course: Calculus III (MTH5102), QMUL
- Teaching associate, demonstrator and marker for undergraduate course: Convergence and Continuity (MTH5104), QMUL
- Teaching associate, demonstrator and marker for undergraduate course: Differential and Integral Analysis (MTH5104), QMUL

**2016**

- Teaching associate, demonstrator and marker for undergraduate course: Convergence and Continuity (MTH5104), QMUL
- Teaching associate, demonstrator and marker for undergraduate course: Differential and Integral Analysis (MTH5104), QMUL
- Ran tutorials for undergraduate course: Introduction to Algebra (MTH4104), QMUL

- Royal Institute Masterclass: Quantum Spacetime, London 2018
- "Einstein's Special Theory of Relativity", Lecture at City Academy Hackney 2018
- Participant and lecturer in QMUL Maths Summer School 2017
- Organised Queen Mary Internal Postgraduate Seminar 2016/2017
- Invitation to send students to Research in UK, Cambridge University 2016