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 distinguished speakers, offering participants the opportunity to engage with current developments at the forefront of the field. In addition to the main lectures, the program will include short talks by graduate students and early-career researchers. The summer school will provide a stimulating and friendly environment, ideal for fostering discussions, collaborations, and the exchange of ideas among researchers at all career stages.
We are pleased to announce that limited funding will be available for early career researchers (PhD students and postdocs) who wish to participate in the summer school and propose to give a talk or a poster presentation. Applicants interested in being considered for funding are invited to include a short abstract of their proposed presentation when registering and send a recommendation letter and a CV to the organisers.
Lecturer: Mathav Murugan (University of British Columbia)
Description
I plan to cover some results on energy measures such as singularity/absolute continuity, its role in the attainment problem for conformal walk dimension (and Ahlfors regular conformal dimension), and also applications to martingale dimension.
Lecturer: Luca Rizzi (SISSA)
Description
Sard's theorem asserts that the set of critical values of a smooth map between finite-dimensional manifolds has measure zero. It is well-known, however, that when the domain is infinite dimensional and the range is finite dimensional, the result is not true. Counterexamples are known already in the class of polynomial maps from an infinite-dimensional Hilbert space to the Euclidean line. The problem is in particular relevant in sub-Riemannian geometry, where the validity of the above property for the endpoint map is the so-called Sard conjecture, and is one of the main open problems in the field. We present an overview of the Sard problem in sub-Riemannian geometry together with some recent results in collaboration with Lerario and Tiberio.
Lecturer: Nageswari Shanmugalingam (University of Cincinnati)
Description
In the non smooth setting of metric measure spaces, where related notions of interest are invariant under bi-Lipschitz transformations of a metric space, negative curvature has a counterpart as Gromov hyperbolicity. This is a coarser, more large-scale notion, but appears to be closely associated with bounded uniform domains via a transformation called uniformization. In this series of lectures we will discuss how such a transformation can link potential theory on Gromov hyperbolic spaces with potential theory on bounded uniform domains. We will begin the course by discussing analogs of Sobolev spaces in non-smooth setting.
Lecturer: Samy Tindel (Purdue University)
Description
In this mini-course I will introduce some basic elements allowing to understand parabolic Anderson models on geometric structures. The topics covered will be:
(1) Gaussian noises and their regularity.
(2) Existence and uniqueness results for the stochastic heat equation.
(3) Moment estimates.
(4) Extensions from Euclidian spaces to hypoelliptic settings, fractals and other geometric contexts.
Notice that I’m not assuming any knowledge of stochastic analysis from the audience. I will try to introduce the objects I’m manipulating in a self-contained way.
If you have any questions, please don't hesitate emailing the organisers @AU ssa2026@math.au.dk
We acknowledge funding from the European Research Council (ERC) under the European Union’s Horizon Europe research and innovation programme (RanGe project, Grant Agreement No. 101199772).
