Discrete geometric analysis

In the first part of this course I will introduce basic concepts and notions in discrete geometric analysis. This includes elementary graph theory, Cayley graphs, random walks and the discrete Laplace operator. After that I will discuss spectral properties and geometric bounds for the eigenvalues of the Laplace operator on finite and infinite graphs. If there is interest, I can also mention some applications of the spectral theory in physics and other fields.

In the second part of the course, I want to discuss more advanced topics and some recent developments in the field, including several discrete notions of curvature, and gradient and heat kernel estimates on graphs.

Date and time info
Friday 14.00 - 15.30

Keywords
discrete Laplace operator, graph theory, eigenvalue and heat kernel estimates, gradient estimates on graphs, discrete notions of curvature, random walks

Prerequisites
linear algebra, analysis, knowledge in graph theory, differential geometry and functional analysis is helpful but not necessary

Audience
MSc students, PhD students, Postdocs

Language
English