by Fabrice Baudoin
📍 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 Continue reading
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. The school will feature a series of five hours lecture courses delivered by Continue reading
Several postdoctoral positions at Aarhus are opening in my group. The earliest possible start date is February 1st 2026, with flexibility for later starts in the spring. These positions are supported by a Villum Investigator Grant and the ERC, offering excellent opportunities Continue reading
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 (ℰ, ℱ = dom(ℰ)) be a Dirichlet form on X. We assume throughout that the heat semigroup Continue reading
Let (X,μ,ℰ,ℱ) be a Dirichlet space and {Pt}t∈[0,∞) denote the associated Markovian semigroup. Throughout the lecture, we shall assume that P_t admits a measurable heat kernel pt(x,y) satisfying, for some C 0 and β 0, for μ × Continue reading
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. We consider the quadratic form ℰ on M, which is obtained as the Continue reading
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). This may be Continue reading
Let (X, ℬ) be a measurable space. We say that (X, ℬ) is a good measurable space if there is a countable family generating ℬ and if every finite measure γ on (X × X, ℬ ⊗ ℬ) can be Continue reading
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) → Continue reading