(Ehemalige) Arbeitsgruppe Konvexe Geometrie

Sekretariat
Kollegiengebäude Mathematik (20.30)
Zimmer 2.056 und 2.002

Karlsruher Institut für Technologie (KIT)
Institut für Stochastik
Englerstr. 2
D-76131 Karlsruhe

Karlsruher Institut für Technologie (KIT)
Institut für Stochastik
Postfach 6980
D-76049 Karlsruhe

Öffnungszeiten:
Mo-Fr, 10:00 Uhr bis 12:00

Tel.: 0721 608 43270/43265

Fax.: 0721 608 46066

# Convex Geometry (Wintersemester 2010/11)

 Dozent: Prof. Dr. Daniel Hug Vorlesung (1044), Übung (1045) 4+2

 Vorlesung: Übung: Montag 11:30-13:00 AOC 201 Dienstag 11:30-13:00 1C-04 Mittwoch 14:00-15:30 1C-03
 Dozent, Übungsleiter Prof. Dr. Daniel Hug Sprechstunde: Nach Vereinbarung. Zimmer 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:

1. Geometric foundations: combinatorial properties, support and separation theorems, extremal representations
2. Convex functions
3. The Brunn-Minkowski Theory: basic functionals of convex bodies, mixed volumes, geometric (isoperimetric) inequalities
4. Surface area measures and projection functions
5. 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.

# 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.