# 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. 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.
2. 6th April 2023
Higgs Centre (JCMB, Kings Buildings)
TBA
TBA
Abstract TBA

## 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.

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".
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

a.d.k.beckett at ed.ac.uk