Sep 05, 2022
26th Internet seminar "Graphs and discrete Dirichlet spaces"
The 26th Internet Seminar on Evolution Equations is devoted to the treatment of graphs and discrete Dirichlet spaces. A graph is a geometric structure on a set of vertices and comes with both a Dirichlet form and a Laplacian defined on the set of functions on its vertices.
We will study the interplay between the geometric structure of a graph (b,c) and the spectral theory of the \ell^2-realisation of the Laplacian as well as properties of the corresponding evolution equation u' = Lu
We expect the participants to have a basic knowledge in functional analysis (bounded operators, uniform boundedness principle, closed graph theorem, Hahn-Banach theorem), on foundations of Hilbert spaces as well as on foundations in complex analysis of one variable.
The concept of the “Internet Seminar” originates in 1998 when Rainer Nagel (Tübingen) organized the first Internet Seminar. Since then, many schools have been organized in the same spirit and the experience of the previous editions has shown that these schools are much more effective than traditional schools where participants have a much more passive role. The course is organised in three phases.
- In Phase 1 (October-February), a weekly lecture will be freely accessible over the internet via the ISEM website. The aim of the lectures is to present the theoretic background which lies behind current ongoing research.
- In Phase 2 (April - June), the participants will form small international groups to work on diverse projects which supplement the theory of Phase 1 and provide some applications of it.
- Finally, Phase 3 (16 July - 22 July 2023) consists in a final workshop in Wuppertal, where the teams will present their projects and additional lectures will be delivered by leading experts.
ISem team
Matthias Keller (Potsdam), Daniel Lenz (Jena), Marcel Schmidt (Leipzig), Christian Seifert (Hamburg)