Title: Equivariant birational geometry of Fano threefolds
Abstract: The notion of G-varieties was introduced by Manin when he studied rationality problems of surfaces over perfect fields in the 1960s. A G-variety is an algebraic variety carrying a generically free regular action from a group G. There are close connections, as well as drastic differences between birational geometry of G-varieties and that of varieties over non-closed fields. In this talk, I will explore these similarities and differences with an emphasis on our work about equivariant unirationality of Fano threefolds from both algebraic and geometric aspects. This is joint work with Yuri Tschinkel and Ivan Cheltsov.