AG Stochastische Geometrie (Sommersemester 2020)
- Dozent*in: Prof. Dr. Daniel Hug, Prof. Dr. Günter Last
- Veranstaltungen: Seminar (0175700)
- Semesterwochenstunden: 2
| Termine | ||
|---|---|---|
| Seminar: | Freitag 9:45-11:15 | SR 2.058 |
| Lehrende | ||
|---|---|---|
| Seminarleitung | Prof. Dr. Daniel Hug | |
| Sprechstunde: Nach Vereinbarung. | ||
| Zimmer 2.051 Kollegiengebäude Mathematik (20.30) | ||
| Email: daniel.hug@kit.edu | Seminarleitung | Prof. Dr. Günter Last |
| Sprechstunde: nach Vereinbarung. | ||
| Zimmer 2.001, Sekretariat 2.056 Kollegiengebäude Mathematik (20.30) | ||
| Email: guenter.last@kit.edu | ||
Studierende und Gäste sind jederzeit herzlich willkommen. Aufgrund der aktuellen Situation bitten wir allerdings um Anmeldung vorab per E-Mail an steffen.winter@kit.edu .
Wenn nicht explizit anders unten angegeben, finden alle Vorträge im Seminarraum 2.58 im Mathebau (Gebäude 20.30) statt.
Freitag, 3.7.2020, Raum 1.067 im Mathebau (Geb. 20.30)
9.45 Uhr Tobias Hartnick (KIT)
Applications of invariant point processes to the study of deterministic Delone sets
Abstract: In our group we study deterministic point sets in proper homogeneous metric spaces like Euclidean or hyperbolic spaces. For example, we are interested in diffraction measures of such point sets or in frequencies of certain patterns. Under some regularity assumptions (“finite local complexity”) on the point set in question, these problems can be approached probabilistically.
Instead of considering our deterministic point set, we consider a random point set, whose local patterns coincide with the given deterministic set, and whose distribution measure is invariant under the isometry group. Invariance of the distribution measure implies that the Palm measure of the random point sets is invariant under a certain countable equivalence relation. The deterministic invariants can then be computed in terms of probabilistic invariants of the random point sets, using an ergodic theorem for this countable equivalence relation.
In my talk I will briefly sketch the deterministic side and then focus on the translation mechanism between deterministic and probabilistic invariants. I will emphasize the qualitative differences between the case, in which the isometry group is amenable, and the case, in which the isometry group is non-amenable.
Freitag, 10.7.2020, Raum 1.067 im Mathebau (Geb. 20.30)
9.45 Uhr Simon Drüssel