Papers & Preprints
My work is in mathematical gauge theory and geometric analysis. I also enjoy interdisciplinary work. I have done work in algebraic geometry, stochastic thermodynamics, and astrophysics. The curriculum vitae carries the complete record, including talks.
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Eliminating the Higgs field and perturbing Yang–Mills connections in cone Yang–Mills theory 2026
In preparation Gauge Theory -
Compactness of Cone Yang–Mills Connections 2026
In preparation Gauge Theory -
Symplectic Yang–Mills Theory 2026
Preprint Gauge Theory On a symplectic manifold, any differential two-form has a natural decomposition into two components: a primitive part and a non-primitive one. Applying this decomposition to the curvature two-form of a principal bundle over a symplectic manifold, we obtain a natural splitting of the Yang–Mills (YM) functional into two functionals that intrinsically depend on the symplectic structure: the primitive Yang–Mills (PYM) functional and the trace Yang–Mills (TYM) functional.
We work out the basic properties of the critical solutions of these two functionals. The PYM functional in particular exhibits many of the desirable properties of the YM functional, including the ellipticity of its Euler–Lagrange equations and an algebraic classification of its flat solutions on \(G\)-bundles. We also prove a monotonicity formula for the PYM functional as a first step towards characterizing its moduli space of solutions.
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On the Resolvent Degree of \(\mathrm{PSL}(n, q)\) 2026
In preparation Algebraic Geometry -
Machine and Deep Learning–driven Angular Momentum Inference from BHEX Observations of the \(n = 1\) Photon Ring 2025
Published Astrophysics The \(n = 1\) photon ring is an important probe of black hole properties and will be resolved by the Black Hole Explorer (BHEX) for the first time. However, extracting black hole parameters from observations of the \(n = 1\) subring is not trivial. We present a framework for the study of \(n = 1\) photon-ring behaviour and black hole property measurement from BHEX images.
Using KerrBAM we generate a grid of \(\gtrsim 10^6\) images of \(n = 1\) photon rings spanning the entire space of Kerr spins and inclinations, and extract intensity profiles with a feature-extraction method developed specifically for BHEX, which outperforms existing Event Horizon Telescope methods by a factor of \(\sim 3000\). Testing spin recovery on simulated images with gradient boosting and with an extension of Deep Horizon, we find \(\gtrsim 90\%\) correct recovery of black hole properties, and characterize the space of resolution-dependent geometric degeneracies. On general relativistic magnetohydrodynamic simulations of accretion flows, both approaches recover spin accurately at the expected inclination of \(\mathrm{M87}^*\).