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 \((n-1)\)?