My research interests are in stochastic analysis and its interaction with quantum field theory, dynamical systems, and data science. I am particularly interested in
Singular stochastic PDEs, regularity structures and rough path theory.
Constructive quantum field theory.
Homogenisation of fast-slow systems.
Path signatures and related methods in machine learning.
You can find my CV here (last updated 8 December 2025).
Distinctions:
2025 Frontiers of Science Award for the article “Stochastic quantisation of Yang-Mills-Higgs in 3D”
Mercator Fellowship 2024-2025, TU Berlin
Rollo Davidson Prize 2024
ERC Starting Grant 2023 – “Stochastic Quantum Gauge Theories”
EPSRC New Investigator Award 2022
2016 Junior Research Fellowship, St John’s College, Oxford
Clarendon Award 2012
From path integral quantization to stochastic quantization: a pedestrian's journey
(with Dario Benedetti, Razvan Gurau)
arXiv:2603.10761
Orthogonal polynomials on path-space
(with Emilio Ferrucci, Darrick Lee, Terry Lyons, Harald Oberhauser, Nikolas Tapia)
arXiv:2602.18808
Large field problem in coercive singular PDEs.
(with Massimiliano Gubinelli)
arXiv:2510.20716
Rates of memory loss for null recurrent Markov chains.
(with Alexey Korepanov)
arXiv:2501.10169
A multiplicative surface signature through its Magnus expansion.
(with Joscha Diehl, Kurusch Ebrahimi-Fard, Nikolas Tapia)
arXiv:2406.16856
Wilson-Itô diffusions.
(with Ismael Bailleul, Massimiliano Gubinelli)
arXiv:2307.11580
Invariant measure and universality of the 2D Yang–Mills Langevin dynamic.
(with Hao Shen)
To appear in Communications on Pure and Applied Mathematics. arXiv:2302.12160
Uniqueness of gauge covariant renormalisation of stochastic 3D Yang-Mills-Higgs.
(with Hao Shen)
Archive for Rational Mechanics and Analysis, 250.11 (2026). arXiv:2503.03060
Local well-posedness of subcritical non-linear heat equations with Gaussian initial data.
(with Hora Mirsajjadi)
Journal of Functional Analysis, 289.12 (2025) 111160. arXiv:2410.11638
Non-Gaussianity of invariant measures to SPDEs in Da Prato-Debussche regime.
(with Ajay Chandra)
Stochastics and Partial Differential Equations: Analysis and Computations (2025) arXiv:2501.06612
Villain action in lattice gauge theory.
(with Christophe Garban)
Journal of Statistical Physics 192, 38 (2025). arXiv:2404.09928
Superdiffusive limits beyond the Marcus regime for deterministic fast-slow systems.
(with Alexey Korepanov, Ian Melbourne)
Communications of the American Mathematical Society 4 (2024), 746-786. arXiv:2312.15734
Norm inflation for the cubic nonlinear heat equation above the scaling critical regularity.
(with Tadahiro Oh, Yuzhao Wang)
To appear in Funkcialaj Ekvacioj. arXiv:2205.14488
Stochastic quantisation of Yang-Mills-Higgs in 3D.
(with Ajay Chandra, Martin Hairer, Hao Shen)
Inventiones Mathematicae 237 (2024) pp 541-696. arXiv:2201.03487
Gauge field marginal of an Abelian Higgs model.
(with Ajay Chandra)
Communications in Mathematical Physics 405.6 (2024) Paper No. 143. arXiv:2207.05443
Algebraic groups in non-commutative probability theory revisited.
(with Kurusch Ebrahimi-Fard, Frédéric Patras)
Infinite Dimensional Analysis, Quantum Probability and Related Topics 27.3 (2024). arXiv:2208.02585
Feature Engineering with Regularity Structures.
(with Andris Gerasimovics, Hendrik Weber)
Journal of Scientific Computing 98.13 (2024). arXiv:2108.05879
Norm inflation for a non-linear heat equation with Gaussian initial conditions.
Stochastics and Partial Differential Equations: Analysis and Computations 12 (2024) pp. 1745–1768. arXiv:2205.14350
A Stochastic Model of Chemorepulsion with Additive Noise and Nonlinear Sensitivity.
(with Ben Hambly, Avi Mayorcas)
Stochastics and Partial Differential Equations: Analysis and Computations 11 (2023) pp. 730-772. arXiv:2106.11165
Signature moments to characterize laws of stochastic processes.
(with Harald Oberhauser)
Journal of Machine Learning Research 23.176 (2022) pp. 1-42. arXiv:1810.10971
Langevin dynamic for the 2D Yang-Mills measure.
(with Ajay Chandra, Martin Hairer, Hao Shen)
Publications mathématiques de l’IHÉS 136, (2022) pp. 1–147. arXiv:2006.04987
Deterministic homogenization under optimal moment assumptions for fast-slow systems. Part 2.
(with Peter Friz, Alexey Korepanov, Ian Melbourne, Huilin Zhang)
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 58.3 (2022) pp. 1328-1350. arXiv:1903.10418
Renormalising SPDEs in regularity structures.
(with Yvain Bruned, Ajay Chandra, Martin Hairer)
Journal of the European Mathematical Society 23.3 (2021) pp. 869-947. arXiv:1711.10239. (The arXiv version fixes a minor error made in the published version.)
Superdiffusive limits for deterministic fast-slow dynamical systems.
(with Peter Friz, Alexey Korepanov, Ian Melbourne)
Probability Theory and Related Fields 178.3-4 (2020) pp. 735-770. arXiv:1907.04825
Persistence paths and signature features in topological data analysis.
(with Vidit Nanda, Harald Oberhauser)
IEEE Transactions on Pattern Analysis and Machine Intelligence 42.1 (2020) pp. 192-202. arXiv:1806.00381
Yang-Mills measure on the two-dimensional torus as a random distribution.
Communications in Mathematical Physics 372.3 (2019) pp. 1027-1058. arXiv:1808.09196
A rough path perspective on renormalization.
(with Yvain Bruned, Peter Friz, Rosa Preiss)
Journal of Functional Analysis 277.11 (2019) 108283. arXiv:1701.01152
An isomorphism between branched and geometric rough paths.
(with Horatio Boedihardjo)
Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 55.2 (2019) pp. 1131-1148. arXiv:1712.01965
Canonical RDEs and general semimartingales as rough paths.
(with Peter Friz)
Annals of Probability 47.1 (2019) pp. 420-463. arXiv:1704.08053
A support and density theorem for Markovian rough paths.
(with Marcel Ogrodnik)
Electronic Journal of Probability 23 (2018), paper no. 56, 16pp. arXiv:1701.03002
Random walks and Lévy processes as rough paths.
Probability Theory and Related Fields 170.3-4. (2018) pp. 891-932. arXiv:1510.09066
Characteristic functions of measures on geometric rough paths.
(with Terry Lyons)
Annals of Probability 44.6 (2016) pp. 4049-4082. arXiv:1307.3580
Constructing supersingular elliptic curves with a given endomorphism ring.
(with Steven Galbraith)
LMS Journal of Computation and Mathematics 17. suppl. A (2014) pp. 71-91. arXiv:1301.6875
On the Number of Facets of Polytopes Representing Comparative Probability Orders.
(with Dominic Searles, Arkadii Slinko)
Order 30.3 (2013) pp. 749-761. arXiv:1103.3938
Stochastic quantisation of Yang-Mills.
Journal of Mathematical Physics, 63.9 (2022), Proceedings of ICMP XX (2021). arXiv:2202.13359.
This is a review article of arXiv:2006.04987 and arXiv:2201.03487.
Multiscale systems, homogenization, and rough paths.
(with Peter Friz, Alexey Korepanov, Ian Melbourne, Huilin Zhang)
VAR75 2016: Probability and Analysis in Interacting Physical Systems, Springer (2019) pp. 17-48. arXiv:1712.01343
Examples of renormalized SDEs.
(with Yvain Bruned, Peter Friz)
Stochastic Partial Differential Equations and Related Fields, Springer (2018) pp. 303-317. arXiv:1701.01158
Rough path theory.
Encyclopedia of Mathematical Physics 2nd Edition
arXiv:2402.10331
Hopf and pre-Lie algebras in regularity structures.
arXiv:2206.14557
A Primer on the Signature Method in Machine Learning.
(with Andrey Kormilitzin)
Signatures Methods in Finance, Springer Finance (2026). arXiv:1603.03788
Symmetries in stochastic Yang–Mills equations.
Oberwolfach report in “Combinatorial and Algebraic Structures in Rough Analysis and Related Fields”. Oberwolfach Rep. 54/2023, 16-18.
Stochastic quantisation of Yang–Mills: state space and Markov process.
Oberwolfach report in “Universality: Random Matrices, Random Geometry and SPDEs”. Oberwolfach Rep. 27/2022, 1513-1514.
A gauge-fixed representation of the 2D Yang–Mills measure.
Oberwolfach report in “New Directions in Rough Path Theory”. Oberwolfach Rep. 40/2020, 21-24.
Characteristic functions of path signatures.
Oberwolfach report in “Rough paths, regularity structures and related topics”. Oberwolfach Rep. 13 (2016), no. 2, 1342-1344.
Characteristic functions of path signatures and applications. Lincoln College, University of Oxford (2016)