Convex Geometry (Winter Semester 2010/11)
- Lecturer: Prof. Dr. Daniel Hug
- Classes: Lecture (1044), Problem class (1045)
- Weekly hours: 4+2
| Schedule | ||
|---|---|---|
| Lecture: | Monday 11:30-13:00 | AOC 201 |
| Tuesday 11:30-13:00 | 1C-04 | |
| Problem class: | Wednesday 14:00-15:30 | 1C-03 |
| Lecturers | ||
|---|---|---|
| Lecturer, Problem classes | Prof. Dr. Daniel Hug | |
| Office hours: Nach Vereinbarung. | ||
| Room 2.051 Kollegiengebäude Mathematik (20.30) | ||
| Email: daniel.hug@kit.edu | ||
Course description
Convexity is a fundamental notion in mathematics which has a combinatorial, an analytic, a geometric and a probabilistic flavour. Basically, a given set in a real vector space is called convex if with any two points of
the segment joining the two points is also contained in
. This course provides an introduction to the geometry of convex sets in a finite-dimensional real vector space.
The following topics will be covered:
- Geometric foundations: combinatorial properties, support and separation theorems, extremal representations
- Convex functions
- The Brunn-Minkowski Theory: basic functionals of convex bodies, mixed volumes, geometric (isoperimetric) inequalities
- Surface area measures and projection functions
- Integral geometric formulas
If time permits, we also consider additional topics such as symmetrization of convex sets or sets of constant width.
Prerequisites
This course is suited for everybody with a firm background in analysis and linear algebra.
Lecture Notes
Cg.pdf|Cg.pdf
Exercise sheets
- Blatt 01.pdf|No 01
- Blatt 02.pdf|No 02
- Blatt 03.pdf|No 03
- Blatt 04.pdf|No 04
- No 05
- No 06
- No 07
- No 08
- No 09
- No 10
- No 11
- No 12
References
- Gruber, P.M. Convex and Discrete Geometry. Grundlehren 336, Springer, 2007.
- Schneider, R. Convex Bodies: The Brunn-Minkowski Theory. Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge, 1993.