Hello, I am currently an Associate Professor at Purdue University. My main focus has been the analysis of singular stochastic partial differential equations, along with connections to statistical mechanics and quantum field theory.
Non-Gaussianity of invariant measures to SPDEs in Da Prato-Debussche regime, with Ilya Chevyrev - Stochastic Partial Differential Equations: Analysis and Computations (2025)
Rough differential equations in the flow approach, with Léonard Ferdinand - Stochastic Processes and Applications (2025)
Rough geometric integration, with Harprit Singh
A priori bounds for 2-d generalised Parabolic Anderson Model, with Guilherme de Lima Feltes, and Hendrik Weber
A flow approach to the generalized KPZ equation, with Léonard Ferdinand
A Stochastic Analysis Approach to Tensor Field Theories, with Léonard Ferdinand - Annales de l’Institut Henri Poincaré - Probabilités et Statistiques (2025)
A Dynamical Yukawa_2 Model, with Martin Hairer and Martin Peev - Communications in Mathematical Physics (2025)
Gauge field marginal of an Abelian Higgs model, with Ilya Chevyrev - Communications in Mathematical Physics (2024)
Stochastic Quantisation of Yang Mills in 3D, with Ilya Chevyrev, Martin Hairer, and Hao Shen - Inventiones Mathematicae (2024)
A priori bounds for rough differential equations with a non-linear damping term, with Timothee Bonnefoi, Augustin Moinat, and Hendrik Weber - Journal of Differential Equations (2022)
Phase transitions for Phi^4_3, with Trishen Gunaratnam and Hendrik Weber - Communications in Mathematical Physics (2022)
Langevin dynamic for the 2D Yang-Mills measure, with Ilya Chevyrev, Martin Hairer, and Hao Shen - Publications Mathématiques de l'IHÉS (2022)
A priori bounds for the Φ^4 equation in the full sub-critical regime, with Augustin Moinat and Hendrik Weber - Archive for Rational Mechanics and Analysis (2023)
Local solution to the multi-layer KPZ equation, with Dirk Erhard and Hao Shen - Journal of Statistical Physics (2019)
The dynamical sine-Gordon model in the full subcritical regime, with Martin Hairer and Hao Shen
Renormalising SPDEs in regularity structures, with Yvain Bruned, Ilya Chevyrev, and Martin Hairer - Journal of the European Mathematical Society (2020)
An analytic BPHZ theorem for regularity structures, with Martin Hairer
Moment bounds for SPDEs with non-Gaussian fields and application to the Wong-Zakai problem, with Hao Shen - Electronic Journal of Probability (2017)
Stochastic PDEs, regularity structures, and interacting particle systems, with Hendrik Weber - Ann. Fac. Sci. Toulouse (2017)
Rigorous quantum field theory functional integrals over the p-adics: anomalous dimensions, with Abdelmalek Abdesselam and Gianluca Guadagni
Hengchang Cao: 2023 -
Martin Peev (co-supervised with Martin Hairer): 2021 - 2025 (expected)
First position after PhD: Postdoc at University of Oxford
Léonard Ferdinand (co-supervised with Vincent Rivasseau): 2022-2024
First position after PhD: Postdoc at Max Planck Institute - Leipzig
Trishen Gunaratnam (co-supervised with Hendrik Weber): 2017-2020
First position after PhD: Postdoc at University of Geneva
Current position: Tenure track assistant professor in mathematics, jointly at Tata Mumbai and ICTS Bangalore