# Sixty-Third Meeting of the North British Mathematical Physics Seminar

The sixty-third meeting of the North British Mathematical Physics Seminar will be held on Saturday 13th November 2021 in Durham, in Room MCS0001 (the Scott Logic lecture theatre) in the Department of Mathematical Sciences. See Google Maps for the location of the department. We plan to stream the meeting live so if you cannot come to Durham, you can still participate.

These people have signed up to attend the meeting in person.

Everyone attending in person must read the building Risk Assessment for the building. Note in particular that inside the building face coverings must be worn at all times except when eating or drinking unless you are except fromk wearing a face covering. The building will be locked. Local participants can enter using their Campus Card. Visitors will need to be admitted at the main entrance (on the north side, the lowest part of the building).

Lunch, as well as morning and afternoon tea, coffee and biscuits will be provided free of charge. However, we need to know numbers in advance so please make sure you email Douglas Smith if you are coming to the meeting, by Friday 5th November if possible. Also register if you want to participate online and the link will be emailed to you.

Limited funds are available to help with travel expenses of participants with no other source of funding. We hope that this will encourage postgraduate students and postdocs to attend the meeting. Please email Benoit Vicedo in advance if you would like to apply for support and please book early to take advantage of the cheaper fares.

To claim expenses complete the Claims Form and Bank Details and email these along with copies of receipts (electronic or scanned) to Benoit Vicedo. Note that participants other than external speakers must get approval in advance as described above.

## Provisional Programme

11:00-11:30
Tea/Coffee
11:30-12:30
Andreas BRAUN (Durham University)

Theories of quantum gravity not only require the absence of ordinary global symmetries, but also of higher form symmetries. We study theories of quantum gravity using F-Theory compactification in which such symmetries are manifestly absent, but can exist in decompactification limits. By examining how the resulting non-compact geometries are glued to the original compact one, we find that there can be unbroken 2-form symmetries even in a compact setting. In a theory of quantum gravity these must hence be gauged. We give further evidence for this proposal using dual perspectives in which gauged 2-form symmetries are mapped to the global structure of the gauge group.

12:30-13:00
Gabriele DIAN (Durham University)

The on-shell superspace formulation of N=4 SYM allows the writing of all possible scattering processes in one compact object called the super-amplitude. Famously, the super-amplitude integrand can be extracted from generalized polyhedra called the amplituhedron. In this talk, I review this construction and present a natural generalization of the amplituhedron that we proved at tree level and conjectured at loop level to correspond to the product of two parity conjugate superamplitudes. The sum of all parity conjugate amplitudes corresponds to a particular limit of the supercorrelator through the Wilson Loop/Amplitude duality. I will conclude by discussing this connection from a geometrical point of view. This talk is based on the recent work arXiv:2106.09372.

13:00-14:00
Lunch
14:00-15:00
Clare DUNNING (University of Kent)

Wronskians of certain orthogonal polynomials arise in a variety of areas including integrable systems, random matrix theory, supersymmetric quantum mechanics and are associated with rational solutions of certain Painleve equations. As well as showing that they play a key role in an example of the ODE/IM correspondence, I'll describe how the combinatorics of the underlying partitions play a curious role in properties of Wronskian polynomials.

15:00-15:30
Daniele FAROTTI (University of Surrey)

The supersymmetry of near-horizon geometries in heterotic supergravity is considered. A necessary and sufficient condition for a solution to preserve more than the minimal $$\mathcal{N} = 2$$ supersymmetry is obtained. A supersymmetric near-horizon solution is constructed which is a $$U(1)$$ fibration of $$AdS_3$$ over a particular Aloff-Wallach space. It is proven that this solution preserves the conditions required for $$\mathcal{N} = 2$$ supersymmetry, but does not satisfy the necessary condition required for further supersymmetry enhancement. Hence, there exist supersymmetric near-horizon heterotic solutions preserving exactly $$\mathcal{N} = 2$$ supersymmetry.

15:30-16:00
Tea/Coffee
16:00-17:00
Ben HOARE (Durham University)

In recent years there has been a proliferation of new integrable sigma-models. Many of these have come from new organisational frameworks and exploiting the tools of deformations and dualities. To retain control of the landscape of models, it helps to understand the relations between them. In this talk we will review two such deformations, the Yang-Baxter deformation of the SSSM and parafermion deformations of the gauged WZW model, and explore how they are related by both duality transformations and scaling limits.

17:00--
Post-meeting discussions in pub and/or over dinner. All are welcome.

## Practical Information

Train information can be obtained here.

For directions to the Department of Mathematical Sciences click here or here. The location is marked here on Google Maps.

Lunch, as well as morning and afternoon tea, coffee and biscuits will be provided free of charge. However, we need to know numbers in advance so please make sure you email Douglas Smith if you are coming to the meeting, by Friday 5th November if possible. Also register if you want to participate online and the link will be emailed to you.

Limited funds are available to help with travel expenses of participants with no other source of funding. We hope that this will encourage postgraduate students and postdocs to attend the meeting. Please email Benoit Vicedo in advance if you would like to apply for support and please book early to take advantage of the cheaper fares.

To claim expenses complete the Claims Form and Bank Details and email these along with copies of receipts (electronic or scanned) to Benoit Vicedo. Note that participants other than external speakers must get approval in advance as described above.

Douglas Smith