Course Content

Prof. François Baccelli will give four one-day short-course lectures, all related to the concept of unimodular random graphs (more generally unimodular random discrete metric spaces), which is currently being developed by several research groups worldwide. This framework is at the interface of randomness, geometry, and ergodic theory. Its implications are ubiquitous beyond mathematics and computer sciences, e.g., in natural sciences. Each course will last about 2 to 4 hours and will include interaction between the lecturer and the audience. The courses will be ”autonomous”, with all necessary concepts introduced at the beginning.

The first lecture will define unimodular random discrete metric spaces and give basic examples. It will introduce the calculus available on these spaces extending, e.g., Palm calculus in Euclidean stochastic geometry. The next two lectures will discuss the following topics in the context of such spaces. Geometry: Extensions of Euclidean Stochastic Geometry, Point Processes, Fractals, Dimensions; Ergodic Theory: Classification of such spaces, Dynamics on such spaces, Indistinguishability. The last lecture will illustrate the ubiquity of such space, in mathematics (Group Theory, Random Walks, Particle Systems) computer science (Stochastic Optimization, Classification) but also in life sciences (Phylogeny, Evolution).

The lectures will primarily be based on joint work with M.-O. Haji Mirsadeghi and A. Khezeli.

Venue

Bayes Centre, Room 4.45

Timetable

Date	Day	Time
27 April 2026	Monday	10:00–14:00
28 April 2026	Tuesday	10:00–14:00
30 April 2026	Thursday	10:00–14:00
1 May 2026	Friday	10:00–14:00