Unifying the Hyperbolic and Spherical 2-Body Problem with Biquaternions

Holographic tensor networks from hyperbolic buildings

We introduce a unifying framework for the construction of holographic tensor networks, based on the theory of hyperbolic buildings. The underlying dualities relate a bulk space to a boundary which can be homeomorphic to a sphere, but also to more general spaces like a Menger sponge type fractal. In this general setting, we give a precise construction of a large family of bulk regions that satisfy complementary recovery. For these regions, our networks obey a Ryu--Takayanagi formula. The areas of Ryu--Takayanagi surfaces are controlled by the Hausdorff dimension of the boundary, and consistentl…

圆盘与球面上不变拉普拉斯算子的谱理论——一种复分析方法

Spectral theory of the invariant Laplacian on the disk and the sphere -- a complex analysis approach

本文通过复分析方法，研究复化单位圆补集上不变拉普拉斯算子的全纯谱理论，给出本征空间闭Möbius不变子空间的内在分类，统一了双曲与球面拉普拉斯算子的本征值理论。