Abstract: For an automorphism f of a smooth projective variety X, Gromov introduced the log-volume growth of f and showed that it coincides with the algebraic/topological entropy of f. In order to study automorphisms of zero entropy, Cantat and Paris-Romaskevich introduced polynomial log-volume growth of f (plov for short) which turns out to be closely related to the Gelfand—Kirillov dimension of the twisted homogeneous coordinate ring associated with (X, f).

This talk will contain 2 parts: in the first part, I will give an optimal upper bound that plov(f) is at most d^2, where d is the dimension of X. This affirmatively answers questions of Cantat--Paris-Romaskevich and Lin--Oguiso--Zhang; in the second part, I will discuss the polynomial growth rate of degree sequences, and show that the growth rate is at most 2d-2, which generalizes a result of Dinh—Lin—Oguiso—Zhang. All results are based on a joint work with Fei Hu.

Registration link：https://www.wjx.cn/vm/wVv3Owl.aspx