I study whether spacetime, gravity, and the particle content of the universe can all emerge from a single underlying algebraic structure. My current work pursues this from two converging directions. The first is through the IKKT (IIB) matrix model — a candidate non-perturbative formulation of string theory where spacetime is not a background but an output, emerging from large-matrix dynamics. With Harold Steinacker at Vienna, I derived modified Einstein equations from the one-loop effective action for 3+1-dimensional quantum branes, finding extra dilaton, axionic, and anharmonicity contributions [CQG 2024]. At cosmological scales these depart significantly from general relativity and generate extra geometric modes reminiscent of dark matter.

The second direction draws on the normed division algebras — ℝ, ℂ, ℍ, 𝕆 — whose structure appears to encode the symmetries and representations of the Standard Model with remarkable precision. Working with Nichol Furey at HU Berlin and with Shahn Majid at QMUL, I am exploring how division-algebraic models and Quantum Riemannian Geometry can be combined to understand whether the Standard Model is algebraically inevitable — emerging from the geometry of quantum spacetime itself rather than imposed by hand.

I study the topological and dynamical structure of vacuum Maxwell fields whose field lines form non-trivial closed knots. These electromagnetic knots carry conserved helicity, finite energy and finite action, and arise naturally from the conformal equivalence between de Sitter space and a compact S³-cylinder — which generates a complete “knot basis” of Maxwell solutions classified by the S³ harmonic spin j. Some of these configurations have since been experimentally realized using laser beams with knotted polarization singularities.

My contributions, developed in collaboration with Olaf Lechtenfeld and others at ITP Hannover, include establishing the knot basis and deriving a clean linear relation between spin and helicity, with a characterisation of the null-field subspace [PLA 2020]; computing all 15 conformal Noether charges for general spin-j combinations, finding that scalar charges either vanish or are proportional to the energy [EPJP 2022]; and numerically tracking the trajectories of charged particles in knotted EM backgrounds, which show intricate sensitivity to initial conditions [JPA 2022].

I construct exact, closed-form solutions of Yang–Mills gauge theory on curved and symmetric spacetimes — de Sitter, anti-de Sitter, and Minkowski via its non-compact coset structure — where standard perturbative intuition fails and symmetry becomes the primary tool. This work, developed with Olaf Lechtenfeld at ITP Hannover, forms the core of my PhD and postdoctoral research.

The answer is yes, when you exploit symmetry systematically. On de Sitter space, equivariant dimensional reduction reduces the Yang–Mills equations to Newton’s problem in a double-well potential, with solutions in terms of Jacobi elliptic functions [thesis, PLB 2022]. On Minkowski space, identifying the SO(1,3) coset structure yields new exact solutions [PLB 2022]; the anti-de Sitter case adds yet another chapter. Alongside this, a Floquet stability analysis of a cosmological Einstein–Yang–Mills–Higgs proposal showed that all perturbative gauge-field eigenmodes up to su(2) spin j = 2 are unstable [NPB 2021].

I study the geometry of spaces where coordinates no longer commute — models of quantum spacetime at the Planck scale where the classical continuum gives way to something irreducibly discrete and “fuzzy.” The natural framework is Connes’ Noncommutative geometry: a spectral triple (non-commutative algebra, Hilbert space, Dirac operator) encodes enough geometric data to define distances between “points” now understood as states of the algebra.

My early work with Biswajit Chakraborty at the S.N. Bose National Centre developed a Hilbert–Schmidt operatorial approach for computing spectral distances on the Moyal plane and the fuzzy sphere — systematically avoiding the star-product ambiguities that affect other methods. On the doubled Moyal plane, we reproduced the Pythagorean distance relation between pure states and showed that a Higgs-like scalar emerges from internal fluctuations of the Dirac operator [PRD 2018]. This thread connects directly to my current project with Shahn Majid at QMUL on Quantum Riemannian Geometry — exploring what a genuinely quantum geodesic looks like and what it implies for particle physics.