Jun 30, 2024, 7:00 PM – Jul 5, 2024, 2:00 PM
SwissMAP Research Station
Le Vernex 9
CH-1865 Les Diablerets
Switzerland
Organized by
Anna Bot (UNIBAS), Fabio Bernasconi (EPFL), Jérémy Blanc (UNIBAS), Zsolt Patakfalvi (EPFL), Julia Schneider (EPFL), Egor Yasinsky (Ecole Polytechnique Paris)
The workshop aims to explore various connections between birational geometry and complex dynamics, focusing on recent achievements in the field. The projective space Pn is one of the most fundamental objects in geometry. Therefore, it is important to understand the structure of its group of birational transformations Bir(Pn), called the Cremona group. In the past 10 years, there have been many impressive results about the structure of this group. For instance, using sophisticated techniques from higher-dimensional geometry, Birkar proved the Borisov-Alexeev-Borisov conjecture and, using his results, Blanc, Lamy and Zimmermann provided in their breakthrough paper a negative answer to an ancient question of Enriques as to whether the Cremona groups are simple.
Developing some bright ideas stemming from dynamical systems and geometric group theory, the works of various mathematicians, such as Cantat, de Cornulier, Dang, Favre, Lesieutre, Lonjou and Urech, allow to study Cremona groups from completely different perspectives, using tools from functional analysis and metric geometry.
The goal of this workshop is to gather world-leading experts in dynamics and birational geometry to further explore these new techniques and to foster new ideas in this flourishing field. A lecture series by Charles Favre on dynamical degrees will give a survey of the recent advances in the study of the Cremona group via dynamical considerations aimed at non-experts. Furthermore, we organise a series of research talks while still allowing sufficient free time to address research problems in small groups and problem sessions for the junior participants.
More information coming soon
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