Arakelov Geometry is a discipline at the crossroad between Number Theory, Complex Analysis and Algebraic Geometry, which aims at bringing geometric intuition to arithmetic. Landmarks of Arakelov Geometry have been the proofs of Mordell conjecture by Faltings and by Vojta, and the equidistribution results by Szpiro, Ullmo and Zhang that led to the proof of Bogomolov conjecture by Ullmo and by Zhang.

In the recent years, the subject has influenced and received influence from many neighboring areas as Diophantine Geometry, Pluripotential Theory, Non-Archimedean and Tropical Geometry, Dynamical Systems and the Theory of Motives, to cite a few. The benefits of these interactions have infused a renewed vitality to the topic, bringing to several remarkable new results, including the proof of the geometric Bogomolov conjecture by Xie and Yuan, and to the uniform Bogomolov and Mordell-Lang conjectures by Dimitrov, Gao and Habegger.

The Intercity Seminar on Arakelov Geometry is an international forum dedicated to the discussion of new advances in Arakelov Geometry. It has been held annually since 2009 (with a few exceptions) in Paris, Kyoto (four times), Barcelona, Rome, Regensburg (twice), Beijing and Copenhagen. The 2022 installment will be the 12th version of this well-established scientific activity. It will be organized by the "Instituto de Ciencias Matemáticas" (ICMAT) and "Institut de Matemàtiques de la Universitat de Barcelona" (IMUB), and will consist of a week-long conference to be held at "La Cristalera", a teaching and research facility located in the countryside near Madrid, and attached to the Universidad Autónoma de Madrid. With its quiet and enjoyable environment, along with the quality service offered by the center, such a place is the ideal venue for the seminar. It offers both conference rooms adapted for the scientific activities and a park outside the structure for shared relaxed moments, which will certainly encourage interactions between the participants.