Mathematical Physics section
Invited speakers:
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Contributed talks:
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Programme:
Mon 30th March, 2026
| 3:00pm – 4:00pm | Christian Korff (Glasgow) |
| “From vertex models to vertex operators” (abstract) | |
| 4:00pm – 4:30pm | Coffee break |
| 4:30pm – 5:30pm | Anne Taormina (KCL) |
| 5:30pm – 6:00pm | Daan Janssen (York) |
| “Quantum reference frames in quantum field theory” (abstract) |
Tue 31st March, 2026
| 3:00pm – 4:00pm | Kasia Rejzner (York) |
| “Measurement and quantum reference frames in QFT” (abstract) | |
| 4:00pm – 4:30pm | Coffee break |
| 4:30pm – 5:00pm | Antonio Moro (Northumbria) |
| “Integrable differential identities for the orthogonal ensemble” (abstract) | |
| 5:00pm – 5:30pm | Christiane Klein (York) |
| “The quantization and Unruh state for Teukolsky scalars on Kerr spacetimes” (abstract) | |
| 5:30pm – 6:00pm | Stefano Galanda (York) |
| “Universal symmetry groups, derived geometry, and higher gauge fields” (abstract) |
Wed 1st April, 2026
| 3:00pm – 4:00pm | Dominic Verdon (Cambridge) |
| “Categorification and operator algebra” (abstract) | |
| 4:00pm – 4:30pm | Coffee break |
| 4:30pm – 5:15pm | Alex Turzillo (Cambridge) |
| “Detection of 2D SPT phases under decoherence” (abstract) | |
| 5:15pm – 6:00pm | Severin Bunk (Hertfordshire) |
| “Universal symmetry groups, derived geometry, and higher gauge fields” (abstract) |
Mathematical Physics section organisers:
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Abstracts:
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Severin Bunk (Hertfordshire): Universal symmetry groups, derived geometry, and higher gauge fields
Many contexts in physics and mathematics feature bundles whose structure groups have higher internal structure. I will survey recent results on the symmetry groups of such bundles and use techniques from derived differential geometry to present a general formalism for connections, or gauge fields, on them. Applications include an equivalence of moduli stacks of supergravity solutions, a new string group model, and an algebraic model for the differential cohomology of smooth manifolds.
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Stefano Galanda (York): Stability analysis of the linearised semiclassical Einstein-Klein-Gordon System: Minkowski spacetime
The semiclassical Einstein equations (SEE) are a nonlinear system of PDEs in which the Einstein tensor is sourced by the renormalised expectation value of a quantum stress–energy tensor. In recent years SEE became an object of study, as they are an effective first-order approximation to a more fundamental, presently unknown, theory of quantum gravity. From a mathematical perspective, the well-posedness of the SEE remains only partially understood, as does the precise characterization of their regime of validity. In this talk, we present a novel approach to the analysis of their linearisation in the case where the stress–energy tensor corresponds to a massive Klein–Gordon quantum field. We prove existence of solutions to the equations linearised around a Minkowski background and carry out a stability analysis. The main mathematical challenges addressed include the construction of a complete gauge fixing for the linearised metric perturbations, the analysis of renormalisation ambiguities via the principle of general local covariance, the proof of existence for a class of non-local hyperbolic equations exhibiting loss of regularity, and the corresponding study of their asymptotic stability. This talk is based on a joint collaboration with Paolo Meda, Simone Murro, Nicola Pinamonti and Gabriel Schmid.
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Daan Janssen (York): Quantum reference frames in quantum field theory
Quantum reference frames (QRFs) formalize a notion of coordinate frames defined relative to a quantum system, and are a key tool in constructing relational observables in quantum theories. We sketch ongoing efforts to characterize relational observables for quantum fields, and discuss how QRFs arise from quantum fields in various contexts. Here we focus in particular on QRFs associated with corner symmetries of gauge theories on spacetimes with (asymptotic) boundaries and corners, and discuss connections to recent developments in defining black hole entropies in quantum gravity.
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Christiane Klein (York): The quantization and Unruh state for Teukolsky scalars on Kerr spacetimes
One of the big open questions in theoretical physics is the quantization of gravity or, as a first step, its linearized version. A major challenge in this process is the large gauge freedom of the theory. However, on Kerr spacetimes, which describe stationary rotating black holes, there is a way to circumvent this issue. Most solutions to the vacuum Einstein equations linearized around a Kerr spacetime can be obtained from spin-weighted, gauge-invariant scalars satisfying the Teukolsky equation of spin \(\pm 2\). Similarly, solutions to the Maxwell- and wave-equations can be related to solutions to the Teukolsky equations of spin \(\pm 1\) and \(0\). Motivated by this, we study the quantization of the spin-s Teukolsky scalars on Kerr spacetimes. We construct an analogue of the physically well-motivated Unruh state for this theory, and show that it is a well-defined Hadamard state. The talk is based on joint work with Dietrich Häfner.
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Christian Korff (Glasgow): From vertex models to vertex operators
We present a novel construction of vertex operators for Schur and Schur's Q-functions using an exactly solvable lattice model from statistical mechanics, the asymmetric six-vertex model. We give a combinatorial description of the boson-fermion correspondence for type A and type B. Our construction works over the integers instead of the rationals and gives new presentations of the vertex operators in terms of hard-core bosons rather than fermions. This is based on joint work with Andrew Hardt and Ben Brubaker.
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Antonio Moro (Northumbria): Integrable differential identities for the orthogonal ensemble
The analysis of integrable differential identities for the partition function and expectation values, combined with ensemble-specific initial conditions, provides an effective and systematic approach to the characterisation of random matrix ensembles, in both the finite-size and thermodynamic regimes.
We illustrate this approach in the case of the orthogonal ensemble. Building on a classical result by Adler and van Moerbeke, who established that the partition function of the orthogonal ensemble is the tau-function of the Pfaff lattice integrable hierarchy, we construct an integrable reduction for the orthogonal ensemble with even nonlinear couplings.
The corresponding initial conditions are evaluated by exploiting a map from orthogonal to skew-orthogonal polynomials, due to Adler, Forrester, Nagao, and van Moerbeke.
We prove that, in the thermodynamic limit, the reduced integrable lattice gives rise to an integrable chain of PDEs of hydrodynamic type. The resulting system possesses a remarkable geometric structure, characterised by the vanishing of the Haantjes tensor and the existence of lower-dimensional reductions in Riemann invariants.
Based on C. Benassi, M. Dell'Atti, A. Moro, “Random Matrix Ensembles and Integrable Differential Identities”. -
Kasia Rejzner (York): Measurement and quantum reference frames in QFT
Mathematical foundations of quantum field theory (QFT) are a very rich source of inspiration for mathematicians from a wide range of different fields of research. One of the frameworks used in this context (started in the 60s) is algebraic quantum fields theory (AQFT), which makes heavy use of operator algebras. More recently, a measurement theory for AQFT has been developed by Fewster and Verch. This opened a gateway for new developments at the intersection of QFT and quantum information theory. Notably, the notion of quantum reference frames (QRFs) has been discussed in the context of AQFT has been discussed in my work with Fewster, Janssen, Loveridge and Waldron. In this talk, I will give an overview of the current progress and outline the future research directions.
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Alex Turzillo (Cambridge): Detection of 2D SPT phases under decoherence
We propose a method of using partial symmetries to distinguish two-dimensional symmetry protected topological (SPT) phases of on-site, unitary symmetries. This novel order parameter takes a wavefunction, such as a ground state of a lattice model, and detects its SPT invariants as expectation values of finitely supported operators, without the need for flux insertion. The method exploits the rotational symmetry of the lattice to extract on-site SPT invariants, building upon prior work on probing crystalline SPT phases with partial rotations. The order parameter is computed analytically on group cohomology models and numerically on a family of states interpolating between the CZX state and a trivial state. Its robustness is suggested by interpreting partial symmetries as generating the topological partition functions of lens spaces. We then adapt the order parameter to the decohered setting, where it detects SPT invariants jointly protected by strong and weak symmetries. We see this explicitly using a class of mixed states obtained from CZX-type models with \(\mathbb{Z}_2 \times \mathbb{Z}_2\) symmetry and subjecting them to noise that weakens one of the \( \mathbb{Z}_2 \) symmetries. Based on arXiv:2503.04510 and arXiv:2507.00127 with Naren Manjunath, Jose Garre-Rubio, and Chong Wang.
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Dominic Verdon (Cambridge): Categorification and operator algebra
In 1996 John C. Baez proposed to ‘categorify’ the definition of a Hilbert space [1]; that is, to define a ladder of definitions of ‘higher’ Hilbert spaces, where a 2-Hilbert space is a category, a 3-Hilbert space is a 2-category, and so on. In this talk I will discuss recent [2][3] and forthcoming work on an infinite-dimensional and manifestly unitary definition of higher Hilbert spaces. I will focus particularly on their bounded operators, and the prospect of a spectral and modular theory analogous to that for von Neumann algebras. Our original motivation for this work was a Tannakian duality theory for locally compact quantum groups, which in the symmetric/classical case would yield a locally compact generalisation of the Doplicher-Roberts theorem. Over the course of the project, however, it became apparent that categorification, and higher category theory more generally, is a structural principle underlying and motivating many definitions and results in the existing theory of operator algebra; this is a key message I will try to communicate in the talk. The talk is based on forthcoming joint work with Robert Allen.
Contact:
All further questions and inquiries can be addressed to Simon Wood at:
- WoodSI at cardiff dot ac dot uk