报告人：王婧教授

题目：ABSOLUTE CONTINUITY OF THE INTEGRATED DENSITY OF STATES IN THE LOCALIZED REGIME

摘要：We establish the absolute continuity of the integrated density of states (IDS) for quasi-periodic Schrödinger operators with a large trigonometric potential and Diophantine frequency. This addresses Eliasson's open problem in 2002, partially solving it. Furthermore, this result can be extended to a class of quasi-periodic long-range operators. Our proof is based on stratified quantitative almost reducibility results of dual cocycles. Specifically, we establish that a generic analytic one-parameter family of cocycles, sufficiently close to constant coefficients, is reducible except for a zero Hausdorff dimension set of parameters. This result affirms Eliasson's conjecture in 2017. This is a joint work with Xu Xu, Jiangong You and Qi Zhou.

报告地点：理学楼401

报告时间：2023年5月19日 上午：9:00-11:00

报告人简介：王婧，南京理工大学教授、博士生导师。主要从事拟周期动力系统方面的研究。在Adv. Math., Comm. Math. Phys., J. Differ. Equ., J. Funct. Anal., Trans. Amer. Math. Soc.等期刊发表论文多篇，先后主持国家自然科学基金青年项目和面上项目，以及江苏省基础研究计划青年基金和优秀青年基金项目，获得第七届“江苏省数学成就奖”。