Students in Theoretical and Mathematical Physics (STAMP)

STAMP is a cross-disciplinary student seminar which launched in August 2022 to bring together PG students working in theoretical and mathematical physics in Edinburgh. It seeks to repair links between the different research groups which were broken during the Covid pandemic, forge new ones, and give PG students a friendly environment to share their research and hear about what their peers are working on.

STAMP is primary aimed at PhD students in EMPG (University of Edinburgh and Heriot-Watt) and the Higgs Centre, but we welcome any students and junior researchers who wish to join us.

The seminars take place at 4pm every Thursday and the locations currently alternates between the Bayes Centre on the central UoE campus and the Higgs Centre, on the 4th floor of the JCMB, on the Kings Buildings campus. As of February 2023, STAMP is hybrid, with Zoom links shared via the mailing list.

The STAMP organisers are grateful for the funding they have recieved from the Higgs Centre and from the School of Mathematics at University of Edinburgh.

STAMP is currently organised by Andrew Beckett, Linden Disney-Hogg and Conor Elrick.

Keeping up with STAMP

You can sign up to our mailing list by following the instructions here. (You may need to enable pop-ups for this link to work.)

You can also join our Slack workspace where we post the talk schedule and share slides, notes etc.

We now have our own page on the Higgs Centre Website! While we're getting things worked out over there, we'll continue to post all information here, but the plan is to migrate everything over there eventually and just keep this as a pointer page.

Talk Schedule

  1. 8th June 2023
    Higgs Centre (JCMB, Kings Buildings)
    Diffusion boundary layer theory
    Freya Bull (UoE, SoPA, Institute for Condensed Matter and Complex Systems)
    When we consider the flow of fluid over a surface, our boundary condition at the surface (no slip - surface velocity is zero) results in the formation of a thin layer of fluid in which the velocity increases rapidly from zero at the surface to a value comparable to the bulk velocity far from the surface. Drawing a parallel to this, when we consider diffusion between a flowing liquid and a surface, the effect of fixing a boundary condition at that surface is the creation of a thin boundary layer, where the concentration changes rapidly, so as to satisfy both the boundary condition at the surface, and match the bulk concentration far from the surface. Since diffusion is (generally) a much slower process than convection, the diffusion boundary layer is much thinner than the convective boundary layer. In this talk I will briefly discuss some of the history of diffusion boundary layer theory, and then show how we can use the theory to solve the convection-diffusion equation for some geometries of laminar flow. Finally, I will discuss how these solutions can lead to (perhaps unexpected) geometry-dependence in the particle flux to the boundaries.

Previous Talks (Since Jan 2023)

  1. 16th February 2023
    Bayes Centre 5.45 (Central Campus)
    Skyrmions in the gauged Sigma model of chiral magnets
    Peter Gerlagh (HWU, EMPG)
    We characterise skyrmions in Bogomolny models of chiral magnets without axisymetry. We show a duality between these Bogomolny models and the specific Bogomolny model wherein the so-called DMI tensor is rank one. The potential in these models have two separate minimums and corresponding stationary vacuums. Exact solutions with skyrmions are built around a domain wall which separates these vacuums. The domain walls themselves can be characterised by a position and an angle.
  2. 23rd February 2023
    No Event (Reading week + SoPA student retreat)
  3. 2nd March 2023
    Bayes Centre 5.45 (Central Campus)
    Pedagogical Introduction to Higher Principal Bundles
    Dominik Rist (HWU, EMPG)
    From the Standard Model of particle physics to condensed matter systems, gauge theories form a powerful framework to understand Nature. Mathematically, gauge fields correspond to connections on principal bundles, which are described by Lie algebra valued 1-forms. String theory considerations motivate the lift of this picture to a categorified setting. Principal bundles are lifted to higher principal bundles (or gerbes) and higher connections are then described by higher degree forms valued in some L-infinity algebra. In this lecture, I will introduce these notions underpinning the geometric framework of higher gauge theory, reviewing elements of higher category theory along the way. In particular, the emphasis in this lecture will be on the cocycle description of gerbes with connection.

    Click here for Dominik's notes.

  4. 9th March 2023
    Higgs Centre (JCMB, Kings Buildings)
    The Bethe ansatz in practice: an application to a minimal model in nonequilibrium statistical physics
    Ivan Lobaskin (UoE, SoPA, Institute for Condensed Matter and Complex Systems)
    Integrable systems are, loosely speaking, models that can be solved exactly using certain standard methods. For quantum and stochastic 1D lattice models, this method is the Bethe ansatz. Despite this, in physics, integrability techniques have a reputation of being excessively formal and opaque. Indeed, even when a formal exact solution is given, it can be a nontrivial task to translate this into meaningful statements regarding physical observables. In an effort to challenge this stigma, in this seminar, I will present a classic calculation, in which the Bethe ansatz is used to directly calculate physical observables for a toy model of nonequilibrium statiscial mechanics. Specifically, I will calculate the long time current statistics in a totally asymmetric simple exclusion process -- the ``Ising model of nonequilibrium statistical physics".

    Ref: arXiv:cond-mat/9809044

  5. 16th March 2023
    Bayes Centre 5.45 (Central Campus)
    Chasing Motes: A Physicist's introduction to Hopf Algebras
    Sam Teale (UoE, SoPA, PPT)
    Hopf Algebras are examples of bialgebras, being both an algebra and coalgebra and are additionally equipped with an endomorphism known as an antipode which is analogous to the map of groups that takes elements to their inverse. These structures have been studied since 1941 first in the field of algebraic topology and have since spread to many fields of mathematics. More recently they have been applied to quantum mechanics and the combinatorics of renormalization of quantum field theories. In this talk I will introduce Hopf algebras for a very general audience; work through a couple of simple examples; and finally, discuss the Motic Hopf algebra and its relevance to my work in renormalization.
  6. 23rd March 2023
    Higgs Centre (JCMB, Kings Buildings)
    A look at some ``Axioms for the category of Hilbert spaces (and linear contractions)''
    Nesta van der Schaaf (University of Edinburgh, School of Informatics, LFCS)
    We'll have a look at a new result that characterises Hilbert spaces (and linear contractions) in terms of categorical axioms that do not refer to probabilities, complex numbers, inner products, continuity, convexity, or dimension. To avoid going into too many technical details, I will try to motivate the axioms and broader research landscape (categorical quantum mechanics) by drawing analogies to familiar terminology of sets and Hilbert spaces. (Based on joint work with Chris Heunen and Andre Kornell.)

    Ref: arXiv:2211.02688

  7. 30th March 2023
    Bayes Centre 5.45 (Central Campus)
    An Introduction to QCD Sum Rules
    Matthew Rowe (UoE, SoPA)
    Abstract: QCD sum rules provide an elegant way of accessing non- perturbative physics using the tools of perturbation theory. In this talk I will attempt a relatively self-contained introduction to QCD sum rules using the classic example of pseudoscalar correlators to calculate meson decay constants. I will then discuss some practical matters and complications and, if time permits, some new applications from my own work.
  8. 6th April 2023
    JCMB 1501 (Kings Buildings)
    Algebraic structures in higher-spin gravity
    Simon Pekar (University of Mons; visiting UoE, EMPG)
    Higher-spin gravity refers to an extension of general relativity involving fields with spin higher than two. The problem of finding a consistent interacting theory of higher-spin gravity can be reformulated into algebraic terms, whose solution is surprisingly simple and rigid. We first describe the construction of a higher-spin symmetry algebra in the case of exact higher-spin symmetry, and make some comments regarding its holographic interpretation. We then turn to the problem of ``slightly broken'' higher-spin symmetry, which involves a certain deformation of the infinite-dimensional symmetry into a $A_\infty$ algebra.
  9. 13th April 2023
    Bayes Centre 5.45 (Central Campus)
    3d gravity as a source of integrable systems and hierarchies
    Juan Carlos Morales Parra (HWU, EMPG)
    In 1988 Witten showed the theory of (pure) General Relativity in 3 dimensions is exactly solvable, using an “equivalent” Chern-Simons formulation. In this talk we will describe the theory using the Newman- Penrose formalism and explicitly show how the equations of motion reduce to an AKNS system, proving in this way its integrability in a more direct way. Then we will see how boundary conditions for higher spin 3d gravity naturally provide hierarchies of integrable systems. Explicitly, we will see how to obtain the mBoussinesq hierarchy from boundary conditions in spin-3 gravity on AdS_3 and how the boundary dynamics of the theory could be completely described in terms of this family of integrable systems.

    Click here for Juan Carlos's slides.

  10. 20th April 2023
    Higgs Centre (JCMB, Kings Buildings)
    Semi-Infinite Cohomology and Potential Applications to Non-Lorentzian Physics
    Girish Vishwa (UoE, EMPG)
    Semi-infinite cohomology, first introduced by Boris Feigin in 1984, was shown to be an invaluable tool in the computation of string theory spectra, since it provides the mathematical setting for BRST cohomology. In this talk, I will provide an elementary introduction to the semi-infinite cohomology of graded Lie algebras, with emphasis on the conditions required for Lie algebras to admit a semi-infinite structure. I will then comment on the possibility of defining a semi-infinite structure on the BMS3 algebra, which would have important implications on recent works in areas such as tensionless strings.

    Click here for Girish's first year annual review report, which includes the material from the talk along with some more discussion about links to physics.

  11. 27th April 2023
    Bayes Centre 5.45 (Central Campus)
    Higher categories, representation theory, and non-invertible symmetries from 6D N=(2,0) SCFTs
    Veronica Pasquarella (University of Cambridge, DAMTP)
    With this talk, I wish to highlight the intertwining nature of higher category theory and gauge theory, with representation theory being the binding element in between them. 6D N=(2,0) SCFTs being the natural realm where this correspondence takes place, I will show that the categorical understanding of class S theories and the emergence of non- invertible symmetries, can be traced back to the behaviour of the condensation of homomorphisms in the Symmetry Topological Field Theory (SymTFT), under suitable adaptation of the gauging-by-condensation procedure.

    Veronica's recent preprint on the same topic as her talk: arXiv:2305.18515

  12. 4th May 2023
    No event (Organisers and planned speaker on GRIFT retreat)
  13. 11th May 2023
    Bayes Centre 5.45 (Central Campus)
    From Landau-Ginzburg to Matrix factorisations and TQFT
    Benjamin Haake (UoE, EMPG)
    Landau-Ginzburg models have been used in various areas of mathematical physics. For example, there is a close link between them and sigma models with Calabi-Yau targets, thus making them interesting for String theory. Without going into details on these motivations, I will present Landau-Ginzburg models as an interesting example of dealing with boundary terms by introducing additional fields on the boundary (while partially preserving supersymmetry). The resulting mathematical structure is matrix factorisation. These can be used to build TQFTs from Landau-Ginzburg models which gives a different perspective on physically known results.
  14. 18th May 2023
    No Event (Postponed)
  15. 25th May 2023
    Bayes Centre 5.45 (Central Campus)
    Lessons from the Black Hole Information Problem
    Benjamin Strittmatter (UoE, EMPG)
    Hawking's information puzzle offers a unique perspective on how the effects of quantum gravity are imprinted on the low energy limit of the theory. Crucially, unitarity of black hole evaporation demands that the entropy of Hawking radiation follows a Page curve. In this talk, I aim to give a pedagogical introduction to the information problem and explain how holography motivates a gravitational prescription of computing the fine-grained entropy of radiation. Equipped with a better definition of entropy, we shall see how the tensions around the information paradox are resolved. Time permitting, I will emphasise the key role islands and replica wormholes play in this process.
a.d.k.beckett at