报告人简介：

赵东升，新加坡南洋理工大学教授，博士生导师。1981年毕业于陕西师范大学数学系，同年师从我国著名数学家王国俊教授攻读硕士；1988年赴英国剑桥大学师从国际著名拓扑学专家Peter Johnstone攻读博士。1994年至今在新加坡南洋理工大学从事教学及数学研究工作。研究领域包括拓扑、序理论、广义积分及Baire函数类，主要研究工作发表在Mathematical Proceedings of the Cambridge Philosophical Society、Proceedings of the American Mathematical Society、Fundamenta Mathematicae、Topology and its Applications、Applied Categorical Structures、Canadian Mathematical Bulletin、Houston Journal of Mathematics、Rocky Mountain Journal of Mathematics、Journal of Mathematical Analysis and Applications等数学期刊上，其中一篇论文获2000年ISI世界经典引文奖，是中国首批获此殊荣的17位数学家之一。

报告简介：

The set R(X) of all topologies on a given set X form a complete lattice with respect to the inclusion order. This complete lattice provides a platform to study topologies satisfying various properties from a new perspective. Given a topological property p, let Rp(X) be the set of all topologies on X having property p. The general problems one may ask include: (1) Is Rp(X) an upper/lower subset? (2) Is Rp(X) closed under infima/suprema? (3) What are the maximal/minimal members of Rp(X)? Such problems have been considered for various separation axioms and compactness. One of the well know result is that the compact Hausdorff topologies are minimal Hausdorff. In this talk, I will first give a survey on some classic results , then present some recent results on sober topologies in R(X). At last , some problems will be illustrated.