PageRank and the geometry of graphs

主讲人 Speaker:Paul Horn
时间 Time: 周五16:30-17:30,2019-11-15
地点 Venue:清华大学近春园西楼三层报告厅

摘要 Abstract

In this talk, we’ll discuss the connection between random walks on graphs, graph spectra and geometric features of networks. As part of this discussion, we’ll talk about PageRank, which is a random walk based method originally developed for web-search. We’ll discuss a way of viewing PageRank as a type of parabolic operator, and will talk about how we can use recently developed notions of graph curvature to prove Harnack-like inequalities to understand the relative importance of different webpages. To do this we develop a gradient estimate for PageRank in the vein of the Li-Yau inequality for positive solutions to the heat equation. (More precisely, our inequality is closer to Hamilton’s gradient estimate for positive solutions.

报告人简介 Profile

Paul Horn,2009年获得了加州大学圣地亚哥分校的博士学位,并先后在埃默里大学和哈佛大学获得博士后学位。他于2013年秋加入了丹佛大学,现为丹佛大学的副教授。他的主要研究方向为组合学,具体来说,他倾向于使用概率、线性代数和几何方法中的概念来理解曲线图。