Research and Lecture notes

This post is about a long paper with Aobo Chen and Li Chen, Riesz transforms on the Vicsek set.

Aarhus University – Department of Mathematics (Ny Munkegade 118, 8000 Aarhus C) Position start: 1 August 2026 (3-year full-time fixed-term: 1 Aug 2026–31 Jul 2029) Join the vibrant Stochastics Group at the Department of Mathematics, Aarhus University, at…

The 6–10 July, 2026, Aarhus Summer School in Analysis and Probability aims to bring together leading experts and young researchers in the areas of analysis, probability theory, and their interactions.

Several postdoctoral positions at Aarhus are opening in my group.

Here are the lecture notes of the minicourse given at NYU Abu Dhabi.

In this lecture let X be a locally compact and complete metric space equipped with a Radon measure μ supported on X.

Let (X,μ,ℰ,ℱ) be a Dirichlet space and {Pt}t∈[0,∞) denote the associated Markovian semigroup.

Contents Riemannian manifolds Carnot groups Sierpinski gasket Cheeger space Riemannian manifolds Let (M,g) be an n-dimensional Riemannian manifold with Riemannian volume measure μ and Riemannian distance d.

Contents Lp theory of semigroups Diffusion operators as generators of Dirichlet forms The Lp theory of heat semigroups Our goal, in this section, is to define, for 1 ≤ p ≤ +∞, Pt on Lp := Lp(X,μ).

Let (X, ℬ) be a measurable space.

Contents Quadratic forms and generators Semigroups and generators A first example: The Dirichlet energy on an open set Quadratic forms and generators Definition A quadratic form ℰ on H is a non-negative definite, symmetric bilinear form 𝒟(ℰ) × 𝒟(ℰ) → ℝ, w…