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(Former) Research group Convex Geometry

Secretariat
Allianz-Gebäude (05.20)
Room 4A-16

Address
Institut für Algebra und Geometrie
Universität Karlsruhe (TH)
Kaiserstr. 89-93
76133 Karlsruhe

Office hours:
Montag bis Freitag, 9:15 Uhr bis 11:15 Uhr

Tel.: ++49 721 608 4 3943

Fax.: ++49 721 608 4 6909

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 A in a real vector space is called convex if with any two points of A the segment joining the two points is also contained in A. 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.


Lecture Notes

Cg.pdf|Cg.pdf


Exercise sheets



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.