65th North British Mathematical Physics Seminar

The 65th meeting of the North British Mathematical Physics Seminar will be held in a hybrid mode (in person at the King's Manor, University of York and online on Zoom) on Thursday 30th June 2022. Zoom invitations will be sent out to the NBMPS list and the groups in the NBMPS network closer to the meeting. See North British Mathematical Physics Seminar for instructions to subscribe to the email list.

The King's Manor is in the centre of the city, 5 minutes' walk from the railway station. To get there, turn left out of the station, under the wall, left over the bridge over the river, then left after 100m at the crossroads (see map). The King's Manor is in Exhibition Square, to the left of the fountain and the city art gallery.

Refreshments will be in the refectory and lunch in cafes nearby. To get to the refectory go through the porters' lodge and up the stone staircase towards the end of the first court on the left. Talks will be in K/133, entered either through the refectory (back of the theatre) or at the far left-hand corner of the furthest court (which brings you in at the front of the theatre).

Programme

Abstract: I will discuss some extensions via Grassmann algebras of certain maps which satisfy the set-theoretic Yang-Baxter equation. I will describe how such maps are obtained from refactorisations of products of Darboux matrices associated to certain integrable PDEs (focusing on the NLS and KdV equations), and I will discuss some integrability properties of the Grassmann extended maps.

Abstract: The affine Gaudin model, associated with an untwisted affine Kac-Moody algebra, is known to arise from a certain gauge fixing of 4-dimensional mixed topological-holomorphic Chern-Simons theory in the Hamiltonian framework. We show that the finite Gaudin model, associated with a finite-dimensional semisimple Lie algebra, can likewise be obtained from a similar gauge fixing of 3-dimensional mixed BF theory in the Hamiltonian framework. Based on joint work arXiv:2201.07300 with B. Vicedo.

Abstract: The classification of anti de Sitter black holes is an open problem of central importance in holography. In this talk I will report recent advances in classification of supersymmetric solutions to five-dimensional minimal gauged supergravity. In particular, we prove a black hole uniqueness theorem for supersymmetric solutions with SU(2) symmetry and an analytic horizon. As part of the proof, we provide a local classification of Kahler spaces admitting SU(2) isometry. Finally, we discuss future generalizations of this result.

Abstract: In the first part of the talk, I will explain that homotopy algebras are ubiquitous in field theory and that they essentially govern all aspects of a theory including classical solutions, symmetries, and scattering theory. In the second part of the talk, I will take homotopy algebras as gauge algebras and formulate higher principal bundles and higher gauge theory.

Abstract: The idea of writing various quantities in gravity as double copies of the analogous objects in Yang-Mills gauge theory has been gaining a lot of traction in recent years - I will give an overview of the numerous different formulations that have arisen from this drive. Then I will focus on 2 particular ones: the first is based on certain double copy replacement rules in the self-dual sector, and the second links with twistor theory. These have allowed for a recent expansion of the remit of the double copy in the context of symmetries and classical solutions. Finally, I will make some comments on a more ambitious question: is it possible to unify the various different formulations into a single framework?

Practical Information

Limited funds are available to help with travel expenses of those with no other source of funding, especially postgraduate students and postdocs. Please book early to take advantage of the cheaper advance-purchase train fares. For how to claim please see the main NBMPS page.

Zoom invitations will be sent out to the NBMPS list and the local groups closer to the meeting.

If you have any questions, please email the local organiser, Benoit Vicedo. There is no need to notify us in order to attend.