Guolei Zhong, Dynamical Characterization of Projective Toric Varieties

As a fundamental building block of the equivariant minimal model program, the rationally connected variety plays a significant role in the classification of projective varieties admitting non-isomorphic endomorphisms. Twenty years ago, Nakayama confirmed Sato’s conjecture that, a smooth projective rational surface is toric if and only if it admits a non-isomorphic endomorphism. In this talk, I will survey some recent progress on a higher dimensional analogue of Nakayama’s result. This talk is based on some joint works with Jia Jia, Sheng Meng and De-Qi Zhang.