Abstract We define the Anderson Hamiltonian H on a two-dimensional manifold using the
high order paracontrolled calculus. It is a self-adjoint operator with pure point spectrum. We …

Paracontrolled calculus and regularity structures I Page 1 c⃝2021 The Mathematical Society of
Japan J. Math. Soc. Japan Vol. 73, No. 2 (2021) pp. 553–595 doi: 10.2969/jmsj/81878187 …

The reconstruction theorem tackles the problem of building a global distribution, on ℝ d or
on a manifold, for a given family of sufficiently coherent local approximations. This theorem …

We prove a general equivalence statement between the notions of models and modeled
distributions over a regularity structure, and paracontrolled systems indexed by the regularity …

The reconstruction theorem, a cornerstone of Martin Hairer's theory of regularity structures,
appears in this article as the unique extension of the explicitly given reconstruction operator …

Based on the notion of paracontrolled distributions, we provide existence and uniqueness
results for rough Volterra equations of convolution type with potentially singular kernels and …

Bony's paraproduct is one of the main tools in the theory of paracontrolled calculus. The
paraproduct is usually defined via Fourier analysis, so it is not a local operator. In the …

First we introduce the Bailleul-Hoshino's result [4], which links the theory of regularity
structures and the paracontrolled calculus. As an application of their result, we give another …

Stochastic partial differential equations (SPDEs) are simply PDEs with noise. Just as there
are many different types of PDEs, there are at least as many different types of SPDEs. In this …

Paracontrolled distributions and singular SPDEs Page 1 Paracontrolled distributions and
singular SPDEs by Nicolas Perkowski March 30, 2020 Abstract These are the lecture notes for …