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Institut für Stochastik

Sekretariat
Kollegiengebäude Mathematik (20.30)
Zimmer 2.056 und 2.002

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

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

Öffnungszeiten:
Mo-Fr 10:00 - 12:00

Tel.: 0721 608 43270/43265

Fax.: 0721 608 46066

Convex Geometry (Sommersemester 2013)

Dozent: Prof. Dr. Daniel Hug
Veranstaltungen: Vorlesung (0152800), Übung (0152810)
Semesterwochenstunden: 4+2


Termine
Vorlesung: Dienstag 14:00-15:30 1C-04
Mittwoch 11:30-13:00 1C-04
Übung: Montag 15:45-17:15 1C-04
Dozenten
Dozent Prof. Dr. Daniel Hug
Sprechstunde: Nach Vereinbarung.
Zimmer 2.051 Kollegiengebäude Mathematik (20.30)
Email: daniel.hug@kit.edu
Übungsleiterin Dr. Ines Ziebarth
Sprechstunde: nach Vereinbarung
Zimmer Allianz-Gebäude (05.20)
Email: ines.ziebarth@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 and to basic properties convex functions. Results and methods of convex geometry are particularly relevant, for instance, in optimization theory and in stochastic geometry.

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 and Exercises

Lecture notes in English (by D. Hug and W. Weil) and exercises are to be found here.


References

  • Gruber, Peter. Convex and Discrete Geometry, Grundlehren der mathematischen Wissenschaften, vol. 336, Springer, Berlin, 2007.
  • Schneider, Rolf. Convex Bodies: the Brunn-Minkowski theory, Cambridge University Press, Cambridge, 1993.