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
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)
arXiv:2302.12160
Uniqueness of gauge covariant renormalisation of stochastic 3D Yang-Mills-Higgs.
(with Hao Shen)
To appear in Archive for Rational Mechanics and Analysis. 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)
Stoch PDE: Anal Comp. (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)
Comm. Amer. Math. Soc. 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.
Stoch PDE: Anal Comp. 12 (2024) pp. 1745–1768. arXiv:2205.14350
A Stochastic Model of Chemorepulsion with Additive Noise and Nonlinear Sensitivity.
(with Ben Hambly, Avi Mayorcas)
Stoch PDE: Anal Comp. 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)
Ann. Inst. H. Poincaré Probab. Statist. 58.3 (2022) pp. 1328-1350. arXiv:1903.10418
Renormalising SPDEs in regularity structures.
(with Yvain Bruned, Ajay Chandra, Martin Hairer)
J. Eur. Math. Soc. 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)
Probab. Theory 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 TPAMI. 42.1 (2020) pp. 192-202. arXiv:1806.00381
Yang-Mills measure on the two-dimensional torus as a random distribution.
Comm. Math. Phys. 372.3 (2019) pp. 1027-1058. arXiv:1808.09196
A rough path perspective on renormalization.
(with Yvain Bruned, Peter Friz, Rosa Preiss)
J. Funct. Anal. 277.11 (2019) 108283. arXiv:1701.01152
An isomorphism between branched and geometric rough paths.
(with Horatio Boedihardjo)
Ann. Inst. H. Poincaré Probab. Statist. 55.2 (2019) pp. 1131-1148. arXiv:1712.01965
Canonical RDEs and general semimartingales as rough paths.
(with Peter Friz)
Ann. Probab. 47.1 (2019) pp. 420-463. arXiv:1704.08053
A support and density theorem for Markovian rough paths.
(with Marcel Ogrodnik)
Electron. J. Probab. 23 (2018), paper no. 56, 16pp. arXiv:1701.03002
Random walks and Lévy processes as rough paths.
Probab. Theory Related Fields. 170.3-4. (2018) pp. 891-932. arXiv:1510.09066
Characteristic functions of measures on geometric rough paths.
(with Terry Lyons)
Ann. Probab. 44.6 (2016) pp. 4049-4082. arXiv:1307.3580
Constructing supersingular elliptic curves with a given endomorphism ring.
(with Steven Galbraith)
LMS J. Comput. Math. 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)
To appear in a Springer volume "Signatures Methods in Finance: An Introduction with Computational Applications" 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)