Convex Geometry (Wintersemester 2010/11)
- Dozent*in: Prof. Dr. Daniel Hug
- Veranstaltungen: Vorlesung (1044), Übung (1045)
- Semesterwochenstunden: 4+2
|Vorlesung:||Montag 11:30-13:00||AOC 201|
|Dozent, Übungsleiter||Prof. Dr. Daniel Hug|
|Sprechstunde: Nach Vereinbarung.|
|Zimmer 2.051 Kollegiengebäude Mathematik (20.30)|
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.
This course is suited for everybody with a firm background in analysis and linear algebra.
- 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.