Acylindricity of the Cremona Group - Lecture 3

Explore the third lecture in a mini-course series on the Cremona group, focusing on its acylindricity. Delve into the group of birational transformations of the projective plane and its action on an infinite-dimensional hyperbolic space. Learn about the key tools used to study this group and understand the proof of its acylindrical hyperbolicity. Discover the implications of this property, including the SQ-universal property, which demonstrates that every countable group can be embedded in a quotient of the Cremona group. Gain insights into advanced mathematical concepts and their applications in group theory during this 42-minute lecture presented at the "Groupes énormes/ Huge Groups" conference.