Acylindricity of the Cremona Group - Part I

Acylindricity of the Cremona Group - Part I

Explore the intricacies of the Cremona group in this 36-minute lecture from the "Groupes énormes/ Huge Groups" conference. Delve into the world of birational transformations of the projective plane, beginning with a gentle introduction to the Cremona group. Examine its action on an infinite-dimensional hyperbolic space, a crucial tool for understanding this mathematical structure. Follow the speaker's journey towards proving the acylindrical hyperbolicity of the Cremona group, uncovering its SQ-universal property. Gain insights into how this property allows every countable group to be embedded in a quotient of the Cremona group, expanding your understanding of group theory and algebraic geometry.