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#### An upper bound for polynomial log-volume growth of automorphisms of zero entropy

AbstractLet f by an automorphism of zero entropy of a smooth projective variety X. The polynomial log-volume growth plov(f) of f is a natural analog of Gromov's log-volume growth of automorphisms (of positive entropy), formally introduced by Cantat and Paris-Romaskevich for slow dynamics in 2020. A surprising fact noticed by Lin, Oguiso, and Zhang in 2021 is that this dynamical invariant plov(f...

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#### Differential Geometry Seminar | Spectral bounds on hyperbolic 3-manifolds

Abstract：I will discuss some new bounds on the spectra of Laplacian operators on hyperbolic 3-manifolds. One example of such a bound is that the spectral gap of the Laplace-Beltrami operator on a closed orientable hyperbolic 3-manifold must be less than 47.32, or less than 31.57 if the first Betti number is positive. The bounds are derived using two approaches, both of which employ linear prog...

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