主持人：张通

报告人简介：
刘世平，中国科学技术大学数学科学学院副院长，教授，博士生导师，曾入选国家青年人才计划。2012年于Max Planck Institute获得博士学位，导师为Jost教授。主要研究兴趣集中在离散几何分析领域，例如由黎曼几何和整体分析中的结果和方法所引导的离散空间相应问题；图论或理论计算机科学等离散数学领域本身所关心且有希望用几何分析方法来解决的问题；在离散空间上发展新方法新结果后应用到连续空间上揭示新发现等。论文发表在Adv. Math.，Crelle's Journal，Mathematical Research Letters等知名数学期刊。

报告摘要：
Given a discrete space with local structural restrictions, it is natural to ask how large can such a space be. This type of problems has been studied for codes, graphs, Markov chains et al. I will give a brief survey on various discrete Ricci curvature notions, with a particular emphasis on their applications in tackling the above mentioned size problem. In particular, we will report recent progresses on the study of conjectures due to Qiao, Park and Koolen and to Terwilliger on sizes of so-called amply regular graphs. We will see that a common feature of various discrete Ricci curvature notions is that they all can be characterized by certain gradient estimate of the heat kernel, but in terms of different function norms.