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(Ehemalige) Arbeitsgruppe Konvexe Geometrie

Sekretariat
Allianz-Gebäude (05.20)
Zimmer 4A-16

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

Öffnungszeiten:
Montag bis Freitag, 9:15 Uhr bis 11:15 Uhr

Tel.: ++49 721 608 4 3943

Fax.: ++49 721 608 4 6909

Convex Geometry (Wintersemester 2010/11)

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


Termine
Vorlesung: Montag 11:30-13:00 AOC 201
Dienstag 11:30-13:00 1C-04
Übung: Mittwoch 14:00-15:30 1C-03
Dozenten
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 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




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.