报告题目：Short time full asymptotic expansion of hypoelliptic heat kernel at the cut locus

报告人：Professor Yuzuru INAHAMA

邀请人：武娟 副教授

报告时间： 2019年3月29日 10:00-11:30

报告地点： 行政楼一楼视频会议室

邀请部门：中国（西安）丝绸之路研究院

报告人简介：   Yuzuru INAHAMA 日本九州大学数学学院教授，主要研究随机分析，Rough Path Theory, Malliavin 积分等，Stochastic Processes and their Applications 副主编，在Ann. Probab., Trans. Amer. Math., Soc., J. Funct. Anal., J. London Math. Soc., Proc. Amer. Math. Soc.等期刊发表SCI论文30余篇。

报告内容： In this talk we prove a short time asymptotic expansion of a hypoelliptic heat kernel on a Euclidean space and a compact manifold. We study the cut locus case, namely, the case where energy-minimizing paths which join the two points under consideration form not a finite set, but a compact manifold. Under mild assumptions we obtain an asymptotic expansion of the heat kernel up to any order. Our approach is probabilistic and the heat kernel is regarded as the density of the law of a hypoelliptic diffusion process, which is realized as a unique solution of the corresponding stochastic differential equation. Our main tools are S. Watanabe's distributional Malliavin calculus and T. Lyons' rough path theory.

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