virtuell

In this talk, we discuss some limitations of the quantum graph approach in defining Dirichlet forms, Laplacians and/or Brownian motions in case when the graph has vanishing edge lengths. Our model set is the stretched Sierpinski gasket, SSG for short. It is the space obtained by replacing every branching point of the Sierpinski gasket by an interval. (It has also been called ``Hanoi attractor``.) As a result, it is the closure of a countable union of intervals and one might expect that a diffusion on SSG is essentially a kind of gluing together the Brownian motions on the intervals. In fact, there have been several works in this direction. However, there still remains, ``reminiscence`` of the Sierpinski gasket in the geometric as well as analytic structure of SSG and the same should therefore be expected for diffusions. This is a joint work with Patricia Alonso Ruiz (Texas A&M University) and Jun Kigami (Kyoto University).

Hörer sollten sich bitte im Moodle-Raum https://moodle.tu-dortmund.de/enrol/index.php?id=23191 des Seminars anmelden. An alle Angemeldeten werden die Zugangsdaten zum meeting geschickt Weitere Vorträge in der Reihe sind unter http://www.mathematik.tu-dortmund.de/lsix/lehre/WiSe2021/GRK-Seminar/index.php einsehbar.

Uta Freiberg

TU Chemnitz