Stochastic and Integral Geometry II (Summer Semester 2007)
- Lecturer: Prof. Dr. Wolfgang Weil (verstorben)
- Classes: Lecture (1550), Problem class (1551)
- Weekly hours: 4+2
Stochastic geometry deals with the development and analysis of stochastic models for complicated geometrical patterns. It combines concepts from probability theory (point processes, random sets) with elements from convex and integral geometry (curvature measures, intrinsic volumes, principal kinematic formula, Crofton formula).
This two-semester course will introduce in some of the basic ideas and results of this exciting and interesting field. In the first part, the basic model in stochastic geometry, the Boolean model, will be introduced. Then, the underlying geometric concepts will be developed, in particular, curvature measures of convex sets and integral geometric formulas for curvature measures will be studied.
A basic knowledge in probability and measure theory is required.
There will be no lecture on monday april 16th. First lecture will be on tuesday april 17th.
| Schedule | |||
|---|---|---|---|
| Lecture: | Monday 11:30-13:00 | Seminarraum 33 | Begin: 17.4.2007, End: 17.7.2007 |
| Tuesday 9:45-11:15 | Seminarraum 33 | ||
| Problem class: | Friday 14:00-15:30 | Seminarraum 33 | Begin: 20.4.2007, End: 20.7.2007 |
| Lecturers | ||
|---|---|---|
| Lecturer | Prof. Dr. Wolfgang Weil (verstorben) | |
| Office hours: | ||
| Room Kollegiengebäude Mathematik (20.30) | ||
| Email: | Problem classes | Dr. Mario Hörig |
| Office hours: | ||
| Room Allianz-Gebäude (05.20) | ||
| Email: Hoerig@math.uni-karlsruhe.de | ||
Exercise Sheets
- Exercise Sheet 1: blatt01.pdf
- Exercise Sheet 2: blatt02.pdf
- Exercise Sheet 3: blatt03.pdf (corrected version from May 10th)
- Exercise Sheet 4: blatt04.pdf
- Exercise Sheet 5: blatt05.pdf
- Exercise Sheet 6: blatt06.pdf
- Exercise Sheet 7: blatt07.pdf
- Exercise Sheet 8: blatt08.pdf
- Exercise Sheet 9: blatt09.pdf
- Exercise Sheet 10: blatt10.pdf
- Exercise Sheet 11: blatt11.pdf
Supplements
- Topological Supplement: topology.pdf
References
- Schneider, R.; Weil, W.: Integralgeometrie (in german), Teubner 1992
- Schneider, R; Weil, W.: Stochastische Geometrie (in german), Teubner 2000
- Stoyan, D.; Kendall, W.S.; Mecke, J.: Stochastic Geometry and Its Applications, 2nd Ed., Wiley 1995
- Weil, W. (Ed.): Stochastic Geometry, Lecture Notes in Mathematics, Springer 2007