演讲人: Frank bauer 博士（哈佛大学数学系）

讲座时间: 2013年12月6日下午14:00-15:00

讲座地点: 信息楼0127室

讲座内容: Abstract:

In 1984 Dodziuk proved a lower bound on the spectrum of the Laplacian on infinite graphs in terms of an isoperimetric constant. Dodziuk’s bound is an analogue of Cheeger’s inequality for manifolds except for the fact that Dodziuk’s estimate also contains an upper bound for the vertex degrees in the denominator. In a later paper Dodziuk and Kendall expressed that it would be desirable to have an estimate without the rather unnatural vertex degree bound. They overcame this problem in by considering the normalized Laplace operator, which is always a bounded operator, instead. However, the original problem of finding a lower bound on the spectrum of unbounded graph Laplace operators that only depends on an isoperimetric constant remained open until today.

In this talk I will use the concept of intrinsic metrics to give a refined definition of the Cheeger constant of a graph. I will use this novel Cheeger constant to prove nontrivial lower bounds for the bottom of the spectrum even if the vertex degrees are unbounded. The talk is based on joint work with Matthias Keller and Radek Wojciechowski.