Title: Dynamics on automorphism groups of compact Kähler manifolds
Speaker: Fei Hu
Speaker Info: National University of Singapore
Brief Description:
Special Note:
Abstract:
Given a compact Kähler manifold X and a biholomorphic self-map g of X, the topological entropy of g defined in dynamical systems is equal to the logarithm of the spectral radius of the pull-back action g* on the cohomology ring H*(X, C) by Gromov (1977) and Yomdin (1987). I will talk about the dynamics on automorphism groups of compact Kähler manifolds in terms of such invariant. In particular, my talk contains the following two directions. First, we generalize a surface result, that is, a parabolic automorphism of a compact Kähler surface preserves an elliptic fibration, to hyperkähler manifolds. We give a criterion for the existence of equivariant fibrations on ‘certain’ hyperkähler manifolds from a dynamical viewpoint. On the other hand, following the known Tits alternative type theorem of Zhang (2009), we start studying virtually solvable groups G of maximal dynamical rank. We generalize a finiteness result for the null-entropy subset of a commutative automorphism group due to Dinh–Sibony (2004). This is based on joint work with T.-C. Dinh, J. Keum, and D.-Q. Zhang.Date: Tuesday, May 23, 2017