Tue, 10 Mar 2026
13:00
13:00
L2
Hodge Structures of Complex Multiplication Type from Rational Conformal Field Theories
Pyry Kuusela,
(Sheffield)
Abstract
Gukov and Vafa have proposed that a conformal field theory describing a string compactification on a manifold is rational (an RCFT) if and only if the manifold admits complex multiplication (CM). We investigate and extend the Gukov-Vafa proposal by constructing Hodge structures of CM type using only RCFT data, without reference to a geometric interpretation.
We use the chiral and boundary states of the RCFT to construct the complex and rational vector spaces underlying the Hodge structure. Using the known notion of Galois symmetry of RCFTs and some elementary Galois theory, we are able to show that these Hodge structures are of CM-type, subject to some technical assumptions that can be verified explicitly for large classes of theories, including those without known geometric interpretation. We also discuss briefly the relation of complex multiplication to arithmetic geometry.
This talk is based on arXiv:2510.25708 with H. Jockers and M. Sarve.
Tue, 05 May 2026
13:00
13:00
L2
The Bootstrap Siege of M-theory
Andrea Guerrieri
(City University )
Abstract
In recent years, analytic and numerical Bootstrap methods have emerged as powerful tools to probe non-perturbative aspects of quantum field theory and quantum gravity. In this talk I will discuss the nonperturbative S-matrix Bootstrap approach to scattering amplitudes in maximal supergravity. After a brief overview of the method, I will review earlier results obtained in this framework, including bounds on the Wilson coefficient of the R^4 operator in D=9,10,11, and the observation that string and M-theory amplitudes appear to lie on the boundary of the allowed bootstrap region. I will then present preliminary results for the higher dimensional corrections like the D^4 R^4 interaction in eleven dimensions and show how the resulting constraints on the non-perturbative M-theory scattering amplitude match expectations from string/M-theory.
Mon, 15 Jun 2026
16:30 -
17:30
L2
TBA
Prof. Jinchao Xu
(King Abdullah University of Science and Technology (KAUST))
Abstract
TBA
This is a joint OxPDE and Numerical Analysis seminar.
Tue, 03 Mar 2026
13:00
13:00
L2
Beyond Wigner - How Non-Invertible Symmetries Preserve Probabilities
Thomas Bartsch
(Oxford )
Abstract
Recent years have seen the expansion of the traditional notion of symmetry in quantum theory to so-called generalised or categorical symmetries, which may in particular be non-invertible. This seems to be at odds with Wigner's theorem, which asserts that quantum symmetries ought to be implemented by (anti)unitary -- and hence invertible -- operators on the Hilbert space. In this talk, we will try to resolve this puzzle for generalised symmetries that are described by (higher) fusion categories. After giving a gentle introduction to the latter, we will discuss how one can associate an inner-product-preserving operator to (possibly non-invertible) symmetry defects and illustrate our construction through concrete examples. Based on the recent work 2602.07110 with Gai and Schäfer-Nameki.
Tue, 24 Feb 2026
13:00
13:00
L2
The Geometry of Gravitational Radiation
Jelle Hartong
(Edinburgh)
Abstract
Future null infinity of an asymptotically flat spacetime is a conformal Carroll manifold. I will not assume any familiarity with Carroll geometry and explain the relevant geometrical notions as we go along. We will consider asymptotic solutions to the 4D vacuum Einstein equations where future null infinity is endowed with the most general Carroll metric data that is allowed by the Einstein equations. This can be used to define an energy-momentum tensor (EMT) at future null infinity by varying a suitably renormalised action with respect to the boundary Carroll metric data. It is shown that the Ward identities obeyed by this boundary EMT agree with the Bondi loss equations that describe the loss of energy and momentum due to the emission of gravitational waves. The metric near future null infinity can be formulated in terms of a Cartan geometry based on the conformal Carroll algebra. The non-vanishing curvatures of said algebra dictate how radiative the spacetime is. For example, the vacuum degeneracy is described by a flat conformal Carroll connection. We will see that the Bondi loss equations can be rewritten as flux-balance laws where the fluxes are determined by the Cartan geometry for the conformal Carroll algebra.
Tue, 10 Feb 2026
13:00
13:00
L2
Dynamics of the Fermion-Rotor System
Vazha Loladze
(Oxford )
Abstract
In this talk, I will examine the dynamics of the fermion–rotor system, originally introduced by Polchinski as a toy model for monopole–fermion scattering. Despite its simplicity, the system is surprisingly subtle, with ingoing and outgoing fermion fields carrying different quantum numbers. I will show that the rotor acts as a twist operator in the low-energy theory, changing the quantum numbers of excitations that have previously passed through the origin to ensure scattering consistent with all symmetries, thereby resolving the long-standing Unitarity puzzle. I will then discuss generalizations of this setup with multiple rotors and unequal charges, and demonstrate how the system can be viewed as a UV-completion of boundary states for chiral theories, establishing a connection to the proposed resolution of the puzzle using boundary conformal field theory.