ISem26

Dear Participants, dear Local Coordinators,

Thank you for your interest in the 26th Internet Seminar entitled “Graphs and discrete Dirichlet spaces”. It is a pleasure for us to see the great number of registered participants. This means, however, that we have a wide range of people attending this course with completely different background. We have decided to keep the lectures at a slow pace in order to enable every participant to follow them. Nevertheless, we hope to keep the interest of all participants awake. The first phase of the internet seminar will be an introductory course on graphs and discrete Dirichlet spaces. Specialized results and deeper ideas will be prolonged to phase two, where small teams will work on particular problems under the guidance of a project coordinator. These projects will be presented at the final workshop in Wuppertal, Germany. Unfortunately, the final workshop in Wuppertal must be limited in size, meaning that it might happen that not every interested student can take part. The main selection criterion for participation will be activity shown during phase one. We kindly invite you all to use the discussion board at our wiki page to ask questions, make comments, remarks, suggestions during the entire course.

We are happy to say that Lecture 01 is uploaded to the web page and you can download it by clicking on the PDF link

https://www.mat.tuhh.de/veranstaltungen/isem26/_media/lecture01.pdf

In this first lecture (as well as in the upcoming lecture next week) we start by looking at finite graphs and get in touch with the main objects in the finite-dimensional situation, namely graphs, forms, Laplacians, resolvents and semigroups.

We kindly ask the team of Kiel to produce the “official” solutions for the exercises of this first lecture. These will be put on the web page so that everyone can check his or her own solution.

Feel free to use the discussion forum on the web page if you have any questions or comments!

Have fun and enjoy reading,

your virtual lecturers.