Stochastic and Integral Geometry I (Winter Semester 2006/07)
- Lecturer: Prof. Dr. Wolfgang Weil (verstorben)
- Classes: Lecture (1044), Problem class (1045)
- 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.
| Schedule | |||
|---|---|---|---|
| Lecture: | Monday 9:45-11:15 | Seminarraum 31 | Begin: 23.10.2006, End: 14.2.2007 |
| Wednesday 9:45-11:15 | Seminarraum 31 | ||
| Problem class: | Monday 15:45-17:15 | Seminarraum 33 | Begin: 30.10.2006, End: 12.2.2007 |
| Lecturers | ||
|---|---|---|
| Lecturer | Prof. Dr. Wolfgang Weil (verstorben) | |
| Office hours: | ||
| Room Kollegiengebäude Mathematik (20.30) | ||
| Email: | Problem classes | PD Dr. Steffen Winter |
| Office hours: Please contact me by email. | ||
| Room 2.049 Kollegiengebäude Mathematik (20.30) | ||
| Email: steffen.winter@kit.edu | ||
Exercise Sheets
- Sheet 1: blatt01.pdf
- Sheet 2: blatt02.pdf
- Sheet 3: blatt03.pdf
- Sheet 4: blatt04.pdf
- Sheet 5: blatt05.pdf
- Sheet 6: blatt06.pdf
- Sheet 7: blatt07.pdf
- Sheet 8: blatt08.pdf
- Sheet 9: blatt09.pdf
- Sheet 10: blatt10.pdf
- Sheet 11: blatt11.pdf
- Sheet 12: blatt12.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 2006 (in print)