Stochastic partial differential equations are ubiquitous in mathematical modeling. Yet, many
such equations are too singular to admit classical treatment. In this article we review some …

We introduce the theory of random tensors, which naturally extends the method of random
averaging operators in our earlier work (Deng et al. in: Invariant Gibbs measures and global …

We review two works [Chandra et al., Publ. Math. l'IHÉS (published online, 2022) and
Chandra et al., arxiv: 2201.03487 (2022)] that study the stochastic quantization equations of …

In this paper, we explore the version of Hairer's regularity structures based on a greedier
index set than trees, as introduced in (Otto et al. in A priori bounds for quasi-linear SPDEs in …

We define a state space and a Markov process associated to the stochastic quantisation
equation of Yang–Mills–Higgs (YMH) theories. The state space S is a nonlinear metric …

We provide a relatively compact proof of the BPHZ theorem for regularity structures of
decorated trees in the case where the driving noise satisfies a suitable spectral gap …

We define a natural state space and Markov process associated to the stochastic Yang–Mills
heat flow in two dimensions. To accomplish this we first introduce a space of distributional …

We establish that global-in-time existence and non-uniqueness of probabilistically strong
solutions to the three dimensional Navier–Stokes system driven by space-time white noise …

We provide an algebraic framework to describe renormalization in regularity structures
based on multi-indices for a large class of semi-linear stochastic PDEs. This framework is …

We introduce a numerical framework for dispersive equations embedding their underlying
resonance structure into the discretisation. This will allow us to resolve the nonlinear …