# Birational Actions of $\mathrm{SL}(n,\mathbb Z)$ I

 Topology of Algebraic Varieties Topic: Birational Actions of $\mathrm{SL}(n,\mathbb Z)$ I Speaker: Serge Cantat Affiliation: Université de Rennes 1; Member, School of Mathematics Date: Tuesday, November 4 Time/Room: 11:00am - 12:30pm/Physics Library, Bloomberg Hall 201

Consider a smooth complex projective variety $M$. To understand the group of birational transformations (resp. regular automorphisms) of $M$, one can use tools from Hodge theory, dynamical systems, and geometric group theory. I shall try to describe several of these techniques by looking at one specific question: if a finite index subgroup of $\mathrm{SL}(n,\mathbb Z)$ acts faithfully on $M$ by birational transformations, is the dimension of $M$ larger than or equal to $(n-1)$?