Como Lake - June 16-20, 2025 

The goal of this school is to show how probabilistic techniques can be applied to the study of central problems in complex geometry.

The inspiration comes from recent developments in the construction of Kähler-Einstein metrics, which have a paramount importance in both geometry and physics, through a probabilistic and statistical mechanical approach. This is one the appearances of probabilistic techniques, particularly statistical mechanics, in complex geometry.

The aim of the school is to give foundational material to understand the interaction between probability and complex geometry, as well as to highlight some of the novel applications mentioned above.

The School aims at presenting a multidisciplinary and innovative approach to the construction of Kähler-Einstein metrics on complex manifolds, combining methods in probability and geometry. We therefore expect a mixed audience, with participants coming from different areas and with backgrounds. Taking this into account, we plan to structure the School as follows:

• we foresee two introductory mini-courses, one in probability and one in complex geometry, of four hours each. They will be integrated by practical sessions of two hours each, where young participants will have the chance to familiarize with the new techniques and deepen their understanding.

• The mini-courses will be followed by two lectures on the main topic of the school; the lectures will last 8 hours each, with 6 hours of theory and 2 hours dedicated to discussion, exercises, or the presentation of case studies.

Lecturers

Rolf Andreasson (Chalmers University of Technology)

Robert Berman (Chalmers University of Technology)

Alessandra Cipriani (University College London)

Eleonora Di Nezza (Sorbonne Université)

Alexander Drewitz (Universität zu Köln)

Frank den Hollander (Leiden University)

Jakob Hultgren (Umeå University)

Bingxiao Liu (Universität zu Köln)

George Marinescu (Universität zu Köln)

Marco Zamparo (Università del Piemonte Orientale)