[main]mg|pages
publications ⋅ presentations ⋅ events ⋅ people
My current main area of research is stochastic analysis, specifically in connection with problems of constructive quantum field theory. The focus is to develop tools and concepts which are suitable to describe and analyse the pathwise behaviour of quantum or random fields, including their description via partial differential equations and renormalization group ideas. More broadly speaking, I'm interested in problems of statistical mechanics of multiscale systems, analysis of PDEs with random terms and homogenisation theory, mathematical quantum mechanics, path-integral formalisms, non-commutative probability and non-commutative geometry. I've also some side interests in formalisation of mathematics.
with H. Koch and T. Oh. Paracontrolled approach to the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity. Journal of the European Mathematical Society, jan 2023. 10.4171/jems/1294
with M. Hofmanová. A PDE Construction of the Euclidean \(\Phi^4_3\) Quantum Field Theory. Communications in Mathematical Physics, apr 2021. 10.1007/s00220-021-04022-0
with L. Galeati. Noiseless regularisation by noise. Revista Matemática Iberoamericana, jul 2021. 10.4171/RMI/1280
with N. Perkowski. The infinitesimal generator of the stochastic Burgers equation. Probability Theory and Related Fields, aug 2020. 10.1007/s00440-020-00996-5
with N. Barashkov. A variational method for \(\Phi^4_3\). Duke Mathematical Journal, 169(17):3339–3415, nov 2020. 10.1215/00127094-2020-0029
with P. Imkeller and N. Perkowski. Paracontrolled distributions and singular PDEs. Forum of Mathematics. Pi, 3:0, 2015. 10.1017/fmp.2015.2
with F. Flandoli and E. Priola. Well-posedness of the transport equation by stochastic perturbation. Inventiones Mathematicae, 180(1):1–53, 2010. 10.1007/s00222-009-0224-4
Ramification of rough paths. Journal of Differential Equations, 248(4):693–721, 2010. 10.1016/j.jde.2009.11.015
Controlling rough paths. Journal of Functional Analysis, 216(1):86–140, 2004. 10.1016/j.jfa.2004.01.002
Notes for the seminar held during the SRQ – Scaling limits, rough paths, quantum field theory research period in 2018 at the Newton Institute, Cambrige
My PhD thesis “Finite-size scaling in non-equilibirum critical phenomena” (University of Pisa, 2002) (pdf)