North British Mathematical Physics Seminar 56

The fifty sixth meeting of the North British Mathematical Physics Seminar will be held on Tuesday 4 June 2019 at the University of York. Coffee/tea will be in G/135 in the Department of Mathematics, on the first floor of James College, with talks in G/020 downstairs.

Programme

1030-1100
Coffee
1100-1200
Alexander Schenkel (Nottingham)
FA vs AQFT

Factorization algebras (FAs) and algebraic quantum field theory (AQFT) are two well-established approaches towards a mathematical description of observables in a quantum field theory. After a brief introduction to both frameworks, I will explain how FAs and AQFTs on globally hyperbolic Lorentzian manifolds are related to each other. More precisely, I will present functorial constructions that (under certain natural hypotheses) map between these two types of theories in both directions. The main result is an equivalence theorem between certain variants of AQFTs and FAs. This is joint work with M. Benini and M. Perin [arXiv:1903.03396].

1200-1345
Lunch
1345-1415
Allan Gerrard (York)
Nested Bethe ansatz for orthogonal and symplectic open spin chains
1415-1445
Bruno Barton-Singer (Heriot-Watt)
A Bogomol'nyi equation for Magnetic Skyrmions

Magnetic skyrmions are topologically non-trivial spin configurations experimentally observed in thin-film magnets, with potential applications to memory storage and computation. I will introduce the basic model and explain how with a specific choice of model parameters a large family of explicit solutions to the Euler-Lagrange equations can be found.

1445-1530
Tea
1530-1600
Philip Glass (Durham)
Cheshire Cat Resurgence in Supersymmetric Quantum Field Theory

Resurgence is a tool for dealing with asymptotic series such as those found in the perturbative expansions used in QFT. Amongst other things it allows us to take the perturbative series and from it calculate the non-perturbative data for the theory. In some SUSY QFTs the asymptotic nature of the series disappears due to cancellations between Feynman diagrams, but the non-perturbative data remains, thus it looks like Resurgence doesn't work here. However, we will see that this is not the case, and with a small SUSY breaking deformation the asymptotic series will reappear, we will be able to calculate all the non-perturbative data. We will then smoothly set the deformation back to zero whilst keeping all the non-perturbative data. We will see this in N=(2,2) on S^2, and time permitting N=2 on S^3.

1600-1700
Anastasia Doikou (Heriot-Watt)
The Grassmannian Gr(N| N+M) AKNS scheme

We consider the generalized Grassmanian AKNS scheme. This is a universal formulation that naturally yields non-commutative versions of NLS-type models, the (m)KdV and (m)KP systems. We employ the universal Darboux-dressing formulation and we derive solutions for the hierarchy of integrable PDEs via solutions of the matrix Gelfand-Levitan-Marchenko equation. We also identify recursion relations that yield the Lax pairs for the whole matrix hierarchy. These results are obtained considering either matrix-integral or general nth order matrix-differential operators as Darboux-dressing transformations. In this framework special links with the Airy and Burgers equations are also discussed. The matrix version of the Darboux transform is also examined leading to the non-commutative version of the Riccati equation. The non-commutative Riccati equation is solved and hence suitable conserved quantities are derived. In this context we also discuss the infinite case of the NLS-like matrix model as it provides a suitable candidate for a quantum version of the usual NLS model.


Practical Information

These maps will get you from the railway station to the University of York (the university-provided one doesn't show the station). The Departement of Mathematics is in building J2 (now James College), on the west campus.

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.

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