241030 Introduction to Analysis on Graphs (S) (WiSe 2025/2026)

Description:
This seminar wants to provide an introduction to the subject of the
discrete Laplace operator on locally finite graphs. The points we aim
to address are

* Definition of infinite weighted graph;
* Definition and basic properties of the discrete Laplace operator
both on finite and infinite graphs;

*

Heat kernel estimates on infinite graph;
*

Stochastic completeness;
*

The Heat equation.

We will adjust the specific topics in order to match the participant's
levels and interests. As bibliography we refer to

* "Introduction to Analysis on Graphs", A. Grigor’yan, AMS
University lecture series volume 71 (2018);

*
* "Graphs and Discrete Dirichlet Spaces”, M. Keller, D. Lenz, R.
K. Wojciechowski, A Series of Comprehensive Studies in Mathematics
volume 358 (2021).

Further research papers will be added depending on the participation
and the interest of the students.

Teilnahmevoraussetzungen, notwendige Vorkenntnisse

Prerequisites: Functional analysis, measure and integration theory.