中国科学院数学与系统科学研究院
数学研究所
数学科学全国重点实验室
偏微分方程研讨班
Speaker: An Zhang（Beihang University）
Inviter: Nguyen Quoc Hung
Language: English
Title: High-dimensional FUP and quantum chaos
Time & Venue: 2026年8月11日（星期二）10：00-11：00 & 南楼N202
Abstract:We derive an explicit formula for the exponent β in the higher-dimensional fractal uncertainty principles (FUP) established by Cohen 2025b. This quantitative version of FUP yields an explicit essential spectral gap for convex co-compact hyperbolic 3-manifolds arising from quasi-Fuchsian groups, which extending the earlier works of Jin-Zhang 2020 (1D) and Tao 2025. We also prove an essential spectral gap for 2D anisotropic quantum open baker's map. This extends the 1D results of Dyatlov--Jin 2017 and the isotropic 2D results of Cohen 2025a. The key ingredient is the anisotropic discrete fractal uncertainty principle (FUP) associated with a 2D anisotropic fractal set called the Bedford--McMullen carpet. We also study the relation between our anisotropic discrete FUP and its continuous counterpart in the spirit of Dyatlov--Jin 2018 and Cohen 2025a. In particular, we prove continuous FUP for 2D anisotropic porous sets, extending the (high-dimensional) isotropic results of Cohen 2025b. To the best of our knowledge, the anisotropic (line) porosity condition---a variant of Cohen's line porosity and stronger than ball porosity---appears to be new to the literature. This is a joint work with Long Jin and Hong Zhang (Tsinghua U).
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