|Date: Monday, April 16, 2018
Location: 3096 East Hall (4:00 PM to 5:00 PM)
Title: Random walks on the Cremona group
Abstract: The Cremona group of birational transformations of P^2 is a classical object in algebraic geometry. In the last decade, incredible progress (by Cantat, Lamy and several others) has been made by combining complex dynamics and geometric group theory, using the action of the Cremona group on an infinite dimensional hyperbolic space. In new work with J. Maher, we use these techniques to study random compositions of birational maps. For instance, we prove that the dynamical degree of random Cremona transformations grows exponentially fast, and we give a characterization of the Poisson boundary for finitely generated subgroups of the Cremona group.
Speaker: Giulio Tiozzo