报 告 人：黄学平

工作单位：南京信息工程大学

报告时间：11月16日上午10:00

报告地点:学院一楼报告厅

报告摘要：

The stability of two sided Gaussian type heat kernel estimates (GE) with respect to bounded perturbations was known through the equivalence of (GE) with volume doubling and Poincare inequalities, thanks to the classical work of Grigor'yan and Saloff-Coste. Utilizing discretization techniques, they went on to investigate the stability under unbounded weighted perturbations, which is also closely related to the branch of weighted norm estimates in harmonic analysis.

In this talk, we discuss a closely related functional inequality, the so called local Sobolev inequality and its stability. It was known that it is equivalent to Gaussian type heat kernel upper bounds. However, its weighted stability is harder than Poincare type inequalities, due to the different scaling properties of two terms appearing. Hopefully some recent developments in harmonic analysis can shed some light on this problem.

报告人简介：

黄学平，男，南京信息工程大学教师、讲师。2005年本科毕业于清华大学物理系，2008年清华大学数学科学系获硕士学位，2011年在德国 Bielefeld大学数学系获博士学位。2013-2014在Jena大学数学与计算机系从事博士后工作，2014-2015在Tohoku大学情报科学研究科 做博士后，2015年加盟南京信息工程大学。研究兴趣：热核估计和Markov过程的相关问题，以及调和分析和几何学。已经在包括《J. Funct. Anal.》、《 Math. Z. 》、《Stochastic Process. Appl.》、《J. Stat Phys 》在内的国际学术刊物上发表多篇SCI论文。