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报告承办单位:数学与统计学院

报告内容:Potential Theory of Subordinate Brownian Motions

报告人姓名:宋仁明

报告人所在单位:美国Illinois大学数学系

报告人职称/职务及学术头衔:教授，博导

报告时间:8月1日16:00–17:00

报告地点:理科楼410

报告人简介：宋仁明, 教授, 1983和1986年毕业于河北大学数学系，获得理学学士和硕士学位; 1993年毕业于佛罗里达大学数学系，获得哲学博士学位。1994年到密西根大学数学系任教，此后分别于1997、2003、2009获得伊利诺斯大学数学系助理教授、副教授和教授职位。宋仁明教授主要从事随机分析和Markov过程研究，任国际期刊《Journal of Korean Mathematical Society》编辑、《llinois Journal of Mathematics》主编，已发表学术论文百余篇。

摘要:Asubordinate Brownian motion can be obtained by replacing the time parameter of a Brownian motion by an independent increasing Levy process (i.e., a subordinator). Subordinate Brownian

Motions form a large subclass of Levy processes and they are very important in various applications. The generator of a subordinate Brownian motion is a function of theLaplacian.In this talk, I will give a survey of some of the recent results in the study of the potential theory of the subordinate Brownian motions. In particular, I will present recent results on sharp two-sided estimates on the transition densities of killedsubordinate Brownian motion in smooth open sets, or equivalently, sharp two-sided estimates on the Dirichlet heat kernels of the generators of thesubordinate Brownian motion.