主講人：許地生 大灣區(qū)大學(xué)副教授

時(shí)間：2025年10月28日16：30

地點(diǎn)：徐匯校區(qū)三號(hào)樓332會(huì)議室

舉辦單位：數(shù)理學(xué)院

主講人介紹：許地生，大灣區(qū)大學(xué)副教授，研究方向：動(dòng)力系統(tǒng)，分形幾何，譜理論，數(shù)學(xué)教育，在Inventiones, Duke Math Journal, J.E.M.S., Annales ENS等頂尖期刊發(fā)表學(xué)術(shù)論文，動(dòng)力系統(tǒng)國(guó)際會(huì)議Beyond Uniform Hyperbolicity 學(xué)術(shù)委員會(huì)成員，2021，2025年IMO中國(guó)國(guó)家集訓(xùn)隊(duì)教練組成員。

內(nèi)容介紹：This is a joint work with Zhenfu Wang and Qi Zhou. We introduce a comprehensive framework for subordinacy theory applicable to long-range operators on ?^2(Z), bridging dynamical systems and spectral analysis. We establish a correspondence between the dynamical behavior of partially hyperbolic (Hermitian-)symplectic cocycles and the existence of purely absolutely continuous spectrum, resolving an open problem posed by Jitomirskaya.

Our main results include the first rigorous proof of purely absolutely continuous spectrum for quasi-periodic long-range operators with analytic potentials and Diophantine frequencies—in particular, the first proof of the all-phases persistence for finite-range perturbations of subcritical almost Mathieu operators—among other advances in spectral theory of long-range operators.

The key novelty of our approach lies in the unanticipated connection between stable/vertical bundle intersections in geodesic flows—where they detect conjugate points—and their equally fundamental role in governing (de-)localization for Schr¨odinger operators. The geometric insight, combined with a novel coordinate-free monotonicity theory and adapted analytic spectral and KAM techniques, enables our spectral analysis of long-range operators.