The lecture presents the interplay of analysis, geometry, probability
and mathematical physics in the realm of graphs. We start with finite
graphs and develop the connection of graphs, their corresponding
quadratic forms, Laplace operators and Markov processes. With these
notions fundamental phenomena of the mathematics of electrostatics and
heat evolution can be studied. Moreover, we take a look at further
properties of the heat equation as well as the connection of spectral
theory and geometry.
- Kursleiter*in: Prof. Dr. Matthias Keller
- Kursleiter*in: Matti Richter