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...
Abstract：In this talk, we first introduce various models to study what a generic 3-manifold looks like. We then focus on the Heegaard splitting model of 3-manifolds, equipped with geometric complexity using Teichmuller metric. The main result is that the Hempel distance of a generic Heegaard splitting goes linearly to the infinity. In particular, generic 3-manifolds are hyperbolic in this mode...
E-mail：qzsy@tsinghua.edu.cn
Address：Qiuzhen College, Tsinghua University, Haidian District, Beijing
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