241030 Introduction to Analysis on Graphs (S) (WiSe 2025/2026)
Contents, comment
-
Description:
This seminar wants to provide an introduction to the subject of the
discrete Laplace operator on locally finite graphs. The points we aim
to address are* Definition of infinite weighted graph;
* Definition and basic properties of the discrete Laplace operator
both on finite and infinite graphs;*
Heat kernel estimates on infinite graph;
*Stochastic completeness;
*The Heat equation.
We will adjust the specific topics in order to match the participant's
levels and interests. As bibliography we refer to* "Introduction to Analysis on Graphs", A. Grigor’yan, AMS
University lecture series volume 71 (2018);*
* "Graphs and Discrete Dirichlet Spaces”, M. Keller, D. Lenz, R.
K. Wojciechowski, A Series of Comprehensive Studies in Mathematics
volume 358 (2021).Further research papers will be added depending on the participation
and the interest of the students.
Requirements for participation, required level
-
Prerequisites: Functional analysis, measure and integration theory.
Teaching staff
Dates ( Calendar view )
| Frequency | Weekday | Time | Format / Place | Period | |
|---|---|---|---|---|---|
| weekly | Mi | 10-12 | 13.10.2025-06.02.2026 |
Subject assignments
| Module | Course | Requirements | |
|---|---|---|---|
| 24-M-AN-ST5a Ausgewählte Kapitel der Analysis 1 | Seminar Selected Topics in Analysis | Study requirement
Graded examination |
Student information |
| 24-M-AN-ST5b Ausgewählte Kapitel der Analysis 2 | Seminar Selected Topics in Analysis | Study requirement
Graded examination |
Student information |
| 24-M-P1 Profilierung 1 | Profilierungsseminar | Study requirement
|
Student information |
| 24-M-P1a Profilierung 1 Teil A | Profilierungsseminar | Study requirement
|
Student information |
| 24-M-P1b Profilierung 1 Teil B | Profilierungsseminar | Study requirement
|
Student information |
| 24-M-P2 Profilierung 2 | Profilierungsseminar | Study requirement
|
Student information |
| 24-M-PWM Profilierung Wirtschaftsmathematik | Profilierungsseminar | Study requirement
|
Student information |
The binding module descriptions contain further information, including specifications on the "types of assignments" students need to complete. In cases where a module description mentions more than one kind of assignment, the respective member of the teaching staff will decide which task(s) they assign the students.
| Degree programme/academic programme | Validity | Variant | Subdivision | Status | Semester | LP | |
|---|---|---|---|---|---|---|---|
| Studieren ab 50 |
- Address:
- WS2025_241030@ekvv.uni-bielefeld.de
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- Notes:
- Additional notes on the electronic mailing lists
- Last update basic details/teaching staff:
- Wednesday, June 25, 2025
- Last update times:
- Wednesday, July 9, 2025
- Last update rooms:
- Wednesday, July 9, 2025
- Type(s) / SWS (hours per week per semester)
- seminar (S) / 2
- Language
- This lecture is taught in english
- Department
- Faculty of Mathematics
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