In February 2018 we decided to start a mini series of seminars for PhD students within the mathematical physics group here at Heriot-Watt. The idea was to introduce the other PhD students to topics that we were interested in and that are, possibly, related to our research.

The idea is that starting on Thursday 8/2 we will meet in T.01 at 4:30pm, after tea time though this is flexible.

The schedule below is provisional and is fairly likely to change.

Date | Speaker | Topic/Title | Abstract/ Summary of the talk |
---|---|---|---|

8/2/18 | Lukas Müller | Higher Geometry | Lukas gave an introduction to abelian bundle gerbs from the point of view of Deligne hypercohomology. |

15/2/18 | Lukas Müller | Non-Associativity in quantum mechanics arising from smooth distributions of magnetic charge | Canonical quantization of a charged particle in the background of a magnetic field with sources on $\mathbb{R}^3$ is possible only if the sources are localised at isolated points in space and Dirac's charge quantization condition is satisfied. In this case wave functions can be realised as sections of a non trivial line bundle.Otherwise the algebra of operators becomes non-associative and there is no way to represent it on a Hilbert space. In this talk we propose to represent it instead on a 2-Hilbert space of sections of a bundle gerbe.To support this proposal we explicitly construct the action of magnetic translation operators on this 2-Hilbert space. In the case of uniform magnetic charge our construction reproduces known results from deformation quantisation. The categorical structures involved naturally encode the 3-cocycle measuring the non-associativity of the representation. This approach to a basic, but yet unsolved physical problem provides an enriched view on quantum mechanics, and we conclude this talk with a short discussion of the questions it poses regarding its physical interpretation. This is joint work in progress with Severin Bunk and Richard J. Szabo. |

8/3/18 | Calum Ross | Spectral curves and Monopoles | I will try and sketch the construction of the spectral curve of a monopole for gauge group $SU(2)$, maybe $SU(n)$ if I have time. To do this we will encounter Euclidean monopoles, their twistor space and how to extract algebrogeometric data from this construction. The talk will be roughly based on these notes and the references therein. In the end we did not get to talking about the spectral curve but did see most of the details of the twistor space construction and a sketch of how it relates to the twistor space of instantons in four dimensions. |

15/3/18 | Philipp Rüter | QFT and the Jones polynomial | Philipp sketched some of the details from Witten's paper "QFT and the Jones polynomial". |

23/3/2018 | Iain Findlay | Integrable Defects in the Liouville Model | N.B. This is on a Friday as it is jointly a PhD seminar. The core of this talk will be the Lax construction of the Liouville model, and the idea of integrable defects in this picture. Combining these two ideas, I will example the effects of the presence of an integrable defect on the Liouville model, comparing it to the effect of a Bäcklund transformation frozen at a specific point in space, and how we can use these to find a solution to the Liouville equation. Based off of the work: https://arxiv.org/abs/1608.04237 |