19114
Seminar
SoSe 14: EM Forschungsseminar "Seminar zur Diskreten Geometrie"
Raman Sanyal
Additional information / Pre-requisites
The organizational meeting will be in the first semester week. If you are interested in the seminar sign-up at
here.
br> Discrete Geometry - Beyond the basics
Possible topics
here.
br> Discrete Geometry - Beyond the basics
Possible topics
- Polytopes of Polytopes: fiber polytopes, mapping polytopes
- Subdivisions of polytopes: secondary and universal polytopes, equidecomposability
- Connections to combinatorics: permutahedra, associahedra, hypersimplices
- combinatorial convexity: matroids and anti-matroids (convex geometries)
- point-line incidences: Sylvester-Gallai problems, Kayeka problems(?)
- colorful combinatorics: Radon, Caratheodory, Tverberg
- Intersections of convex sets: Helly, Fractional Helly
- Hyperplane arrangements: levels, zonotopes, pseudo-arrangements, Bohne-Dress
- Dualities and polarity: LP-duality, polarity, Gale duality, Alexander duality
- rigidity and the Lower Bound Theorem: stress, Lawrence, LBT
- relations to combinatorial optimization: Birkhoff and friends; transportation polytopes; Schur-Horn Theorem
- tropical convexity and polytopes
- geometric constructions: wedge products and subdirect products/sums
- incidence geometry and Lawrence polytopes
- quotients of polytopes and neighborly polytopes
- Minkowski sums and the Cayley trick
Comments
Inhalt:
In this seminar we will explore advanced notions and constructions from discrete geometry. In particular, we will explore connections to other areas. Students should have a good background in discrete geometry or discrete mathematics (such as 'Discrete Geometry I' or 'Discrete Mathematics I').
close14 Class schedule
Regular appointments
Tue, 2014-04-15 16:00 - 18:00
Tue, 2014-04-22 16:00 - 18:00
Tue, 2014-04-29 16:00 - 18:00
Tue, 2014-05-06 16:00 - 18:00
Tue, 2014-05-13 16:00 - 18:00
Tue, 2014-05-20 16:00 - 18:00
Tue, 2014-05-27 16:00 - 18:00
Tue, 2014-06-03 16:00 - 18:00
Tue, 2014-06-10 16:00 - 18:00
Tue, 2014-06-17 16:00 - 18:00
Tue, 2014-06-24 16:00 - 18:00
Tue, 2014-07-01 16:00 - 18:00
Tue, 2014-07-08 16:00 - 18:00
Tue, 2014-07-15 16:00 - 18:00
Inhalt:
In this seminar we will explore advanced notions and constructions from discrete geometry. In particular, we will explore connections to other areas. Students should have a good ... read more