演讲人：Grigoryan、胡家信、孙玉华

讲座时间：2016-09-21 14:30:00

讲座地点：信息楼三层343研讨室

讲座内容

2016“几何分析小型研讨会”由中国人民大学信息学院主办。为加强几何分析及相关研究领域的学术交流与合作，我们邀请了3位专家学者在人大做报告，研讨会将于2016年9月21日在人大信息楼召开，欢迎广大师生参加。

组委会成员：刘丽光，林勇。

14:30-15:30 Grigoryan（University of Bielefeld, Germany）

Path complexes and their homologies

(Abstract: We introduce the notion of a path complex and define its homology groups. Particular cases of path complexes are simplicial complexes and directed graphs. We discuss some properties of path homologies, in particular, the Kunneth formulas for Cartesian product and join of path complexes.)

15：30-16：10 胡家信（清华大学）

Two-sided sub-Gaussian estimates of heat kernels on intervals for self-similar measures with overlaps.

(Abstract: We obtain two-sided sub-Gaussian estimates of heat kernels for strongly local Dirichlet forms on intervals, equipped with self-similar measures generated by iterated function systems (IFS's) that do not satisfy the open set condition (OSC) and have overlaps. We first give a framework for heat kernel estimates on intervals, and then consider two examples of self-similar measures to illustrate this phenomenon. We make use of Strichartz second-order identities defined by the auxiliary IFS's to compute measures of different-level cells. These auxiliary IFS's do satisfy the OSC and are used to define new metrics. Joint with Qingsong Gu (Hong Kong) and Sze-Man Ngai (USA))

16：10-16：50 孙玉华（南开大学）

On nonnegative solutions to elliptic differential inequalities on Riemannian manifolds

(Abstract：We provide optimal condition in terms of the volume growth of a Riemannian manifold that ensuresthat any non-negative solution to some elliptic differential inequalities on this manifold is identically equal to 0.)