SUBJECT
Title
Convex geometry
Type of instruction
lecture + practical
Level
master
Faculty
Part of degree program
Credits
6+3
Recommended in
Semesters 1-4
Typically offered in
Autumn/Spring semester
Course description
- Convex polytopes, Euler and Dehn–Sommerville formulas, upper bound theorem.
- Mean projections. Isoperimetric, Brunn-Minkowski, Alexander-Fenchel, Rogers–Shephard and Blaschke-Santalo inequalities.
- Lattices in Euclidean spaces. Successive minima and covering radius. Minkowski, Minkowski–Hlawka and Mahler theorems. Critical lattices and finiteness theorems. Reduced basis.
Readings
- B. Grünbaum: Convex polytopes, 2nd edition, Springer-Verlag, 2003.
- P.M. Gruber: Convex and Discrete Geometry, Springer-Verlag, 2006.
- P.M. Gruber, C.G. Lekkerkerker: Geometry of numbers, North-Holland, 1987.