题 目：An introduction to Anderson Localization
摘 要: Anderson localization for the Anderson model can be proved in several different ways if the common distribution of i.i.d.r.v. is absolutely continuous. Without this condition, it remains an open question for d>1 and the number of approaches drop dramatically for d=1. Here we introduce the history of development of proving Anderson localization, focus on two main approaches: MSA and FMM.
时 间： 2018年12月17日 2:30-3:30
题 目：A non-perturbative short proof of Anderson localization In 1d Anderson model
摘 要: Anderson localization for 1d Anderson model with arbitrary disorder (including Bernoulli case) was first proved in 1987 with Multi-Scale Analysis method. Here we provide a very short new non-perturbative proof based on positivity and subharmonicity of Lyapunov exponent. This way of proof avoids the redundant estimates in MSA and still solve the problem with arbitrary disorder. We also derive a uniform version of Craig-Simon estimates which works in high generality and may be of independent interest.
时 间： 2018年12月17日 3:30-4:30
题 目：An introduction to Orthogonal Polynomial on the Unit Circle
摘 要: Orthogonal Polynomial on the unit circle was deeply studied by Barry Simon and it's similarity with Schordinger operators has drawn his attention on exploring the Anderson localization phenomenon on the random OPUC model. Here we develop the basics We need for understanding OPUC including Verblunsky Theorem.
题 目：Anderson localization of random OPUC model
摘 要: The deep similarity between Schordinger operator and OPUC has inspired us to prove Anderson localization for the OPUC using the non-perturbative methods we gave previously for discrete schordinger operators. However, the four diagonal structure and non-unitary property of the restricted operator cause some extra efforts. Here we introduce the non-perturbative short proof of Anderson localization on OPUC and how we get over those problems.
时 间：2018年12月18日 11:00-12:00