Author Archives: Fabrice Baudoin

Assistant Professor in Probability Theory & Stochastic Analysis

Posted on November 8, 2025 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 →

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Aarhus Summer School in Analysis and Probability

Posted on October 22, 2025 by Fabrice Baudoin

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 →

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Postdoctoral Positions in Probability Theory and Analysis

Posted on August 19, 2025 by Fabrice Baudoin

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 →

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Lecture notes: A short introduction to Dirichlet spaces

Posted on January 26, 2025 by Fabrice Baudoin

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

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Lecture 7. Further topics

Posted on January 21, 2025 by Fabrice Baudoin

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 →

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Lecture 6. Gagliardo-Nirenberg inequalities in Dirichlet spaces

Posted on January 19, 2025 by Fabrice Baudoin

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 →

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Lecture 5. Examples of Dirichlet spaces

Posted on January 17, 2025 by Fabrice Baudoin

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 →

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Lecture 4. The Lp theory of semigroups and diffusion operators as generators of Dirichlet forms

Posted on January 15, 2025 by Fabrice Baudoin

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 →

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Lecture 3. Markov semigroups and Dirichlet forms

Posted on January 11, 2025 by Fabrice Baudoin

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 →

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Lecture 2. Quadratic forms in Hilbert spaces

Posted on January 9, 2025 by Fabrice Baudoin

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 →

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