Birational Actions of \(\mathrm{SL}(n,\mathbb Z)\) II

Topology of Algebraic Varieties
Topic:Birational Actions of \(\mathrm{SL}(n,\mathbb Z)\) II
Speaker:Serge Cantat
Affiliation:Université de Rennes 1; Member, School of Mathematics
Date:Tuesday, November 11
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 \((n-1)\)?