Boundedness of algebraic varieties       
-- Chenyang Xu, February 11, 2011

<p>                                                               

I would like to talk about a recent result which
verifies a conjecture of Alexeev and Koll&aacute;r.    
The applications include a linear bound on the orders of the
automorphism groups of general type varieties,    
Shokurov's ACC conjecture on log canonical thresholds, and
boundedness of higher dimensional stable schemes     
and certain Fano varieties. This is joint work with
Christopher Hacon and James McKernan.