Title: Boundedness of algebraic varieties
Speaker: Chenyang Xu
Speaker Info: MIT
In the 19 century, Hurwitz proved that for any compact Riemann surface of genus g>1, the order of its automorphism group is bounded by 84(g-1).Date: Tuesday, January 25, 2011
We prove a natural generalization of this result to all dimensions. In fact, this generalization itself is a special case of a conjecture on volumes of algebraic varieties due to Alexeev-Koll\'ar.
Our work verifies this conjecture. If time permits, I will talk about various other applications to justify that our results play important roles in the study of birational geometry and related fields.
This is joint work with Christopher Hacon and James McKernan.