Absolutely continuity of the IDS for quasi-periodic long-range operators with trigonometric polynomials and large coupling constant
数学公众报告(120周年校庆系列第35场)
报告题目(Title)：Absolutely continuity of the IDS for quasi-periodic long-range operators with trigonometric polynomials and large coupling constant
报告人(Speaker)：王婧 教授 （南京理工大学）
地点(Place)：腾讯会议ID：771-199-065
时间(Time)：2022 年 9月 9 日 下午4:00-5:00
邀请人(Inviter)：黎雄
报告摘要
In this talk, we consider the quasi-periodic long-range operator on \ell^2(\Z^d), in which Schrodinger operator is a special case, with trigonometric polynomial potential and large coupling constant. We use Aubry Duality to transform the operator with large coupling to generalized Schrodinger operator on a strip with small coupling. We first use KAM iteration to get the reducibility for the dual cocycle with all parameters except a Hausdorff zero dimension set, provided the coupling is sufficiently small. Then we get the absolutely continuity of the integrated density of states (IDS) for the dual and the original operators. This is a joint work with Xu Xu, Jiangong You and Qi Zhou.
主讲人简介
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”。
