题目：On the topological entropy of saturated sets for amenable group actions (I)
报告人 任宪坤（重庆大学）
时间：2020年11月26日 14：00-14：50
地点：纯水楼301
摘要：Let $(X,\rho,G)$ be a $G-$action topological system, where $G$ is a countable infinite discrete amenable group and $X$ a compact metric space. We prove a variational principle for topological entropy of saturated sets for systems which have specification and uniform separation properties. This is a joint work with Xueting Tian and Yunhua Zhou.
题目：On the topological entropy of saturated sets for amenable group actions (II)
报告人 任宪坤（重庆大学）
时间：2020年11月26日15：00-15：50
地点：纯水楼301
摘要：We show that certain algebraic actions satisfy these two conditions in part (I).
题目：On the topological entropy of saturated sets for amenable group actions (III)
报告人 任宪坤（重庆大学）
时间：2020年11月26日 16：00-16：50
地点：纯水楼301
摘要：We further discuss the application in multifractal analysis.
题目：A new class of definitive screening designs using Paley's conference matrices
报告人：刘思序 (清华大学)
时间：2020年11月27日09：00-09：50
地点：纯水楼301
摘要：Definitive screening designs constructed by conference matrices guarantee many desirable properties for investigating quantitative factors with three levels. However, the aliasing structure among two-factor interaction terms of such designs is rather complex and varies considerably when adopting different conference matrices of the same order. A new class of definitive screening designs is proposed here, based on Paley's conference matrices. Its theoretical basis and design optimality are obtained. It is proven to be optimal in the sense of Schoen, Eendebak and Goos [Ann. Statist. 47 (2019) 1179–1202]. This is a joint work with Yaping Wang and Dennis K.J. Lin.
题目：A new reformulation of two-dimensional projection uniformity with application to space-filling designs (I)
报告人：刘思序 (清华大学)
时间：2020年11月27日10：00-10：50
地点：纯水楼301
摘要：Space-filling designs are frequently used in both computer and physical experiments. Unifrom designs are a commonly used space-filling designs which minimizes the discrepancy in the overall design space. However, a uniform design may have bad low-dimensional projections, which is undesirable when only a few factors are active. In this paper we focus on a new criterion, called uniform projection criterion, which focuses on two-dimensional projection uniformity. We establish a general reformulation of the average two-dimensional L2 type discrepancy defined by a reproducing kernel, which builds a new link between the relationships of rows and columns of the design. We also connect the the commonly used generalized discrepancy (including the star discrepancy, centered L2 discrepancy, wrap-around L2 discrepancy and mixture discrepancy with the Lp-distance of the designs.
题目：A new reformulation of two-dimensional projection uniformity with application to space-filling designs (II)
报告人：刘思序 (清华大学)
时间：2020年11月27日11：00-11：50
地点：纯水楼301
摘要：Based on the above theoretical results, we provide two constructions of optimal space-filling designs based on generalized Hadamard matrices and perpendicular difference arrays.
题目：SRB measures for partially hyperbolic expanding flows I-mostly expanding case
报告人：糜泽亚 （南京信息工程大学）
时间：2020年11月27日16：00-16：50
地点：纯水楼301
摘要：For a partially hyperbolic flows, we prove that if the center bundle admits the sectionally expanding condition w.r.t. any Gibbs u-state, then there are finitely many SRB/physical measures with basin covering property.
题目：Horseshoes and Lyapunov exponents for Banach cocycles over nonuniformly hyperbolic systems
报告人：邹瑞（南京信息工程大学）
时间：2020年11月27日17：00-17：50
地点：纯水楼301
摘要：Let f be a non-uniformly hyperbolic system with positive entropy, and let A be a Holder continuous cocycle of injective bounded linear operators acting on a Banach space. We prove that there is a sequence of horseshoes for f and dominated splittings for A on the horseshoes, such that not only the measure theoretic entropy of f but also the Lyapunov exponents of A can be approximated by the topological entropy of f and the Lyapunov exponents of A on the horseshoes, respectively.
邀请人：廖刚