19202001
Lecture
WiSe 14/15: Diskrete Geometrie I
Raman Sanyal
Information for students
Klausurtermin am 11.02.2015, 10-12 Uhr im Raum 001 A3/Hörsaal
Additional information / Pre-requisites
Solid background in linear algebra. Knowledge in combinatorics and geometry is advantageous.
Comments
This is the first in a series of three courses on discrete geometry. The aim of the course is a skillful handling of discrete geometric structures including analysis and proof techniques. The material will be a selection of the following topics:
Basic structures in discrete geometry
polyhedra and polyhedral complexes
configurations of points, hyperplanes, subspaces
Subdivisions and triangulations (including Delaunay and Voronoi)
Polytope theory
Representations and the theorem of Minkowski-Weyl
polarity, simple/simplicial polytopes, shellability
shellability, face lattices, f-vectors, Euler- and Dehn-Sommerville
graphs, diameters, Hirsch (ex-)conjecture
Geometry of linear programming
linear programs, simplex algorithm, LP-duality
Combinatorial geometry / Geometric combinatorics
Arrangements of points and lines, Sylvester-Gallai, Erdos-Szekeres,
Szemeredi--Trotter
Arrangements, zonotopes, zonotopal tilings, oriented matroids
Examples, examples, examples
regular polytopes, centrally symmetric polytopes
extremal polytopes, cyclic/neighborly polytopes, stacked polytopes
combinatorial optimization and 0/1-polytopes
For students with an interest in discrete mathematics and geometry, this is the starting point to specialize in discrete geometry. The topics addressed in the course supplement and deepen the understanding for discrete-geometric structures appearing in differential geometry, topology, combinatorics, and algebraic geometry. close
Basic structures in discrete geometry
For students with an interest in discrete mathematics and geometry, this is the starting point to specialize in discrete geometry. The topics addressed in the course supplement and deepen the understanding for discrete-geometric structures appearing in differential geometry, topology, combinatorics, and algebraic geometry. close
Suggested reading
32 Class schedule
Additional appointments
Thu, 2015-04-16 12:00 - 14:00Nachklausur
Location:
Hs 001/A3 Hörsaal (Arnimallee 3-5)
Regular appointments
Tue, 2014-10-14 10:00 - 12:00
Tue, 2014-10-21 10:00 - 12:00
Tue, 2014-10-28 10:00 - 12:00
Tue, 2014-11-04 10:00 - 12:00
Tue, 2014-11-11 10:00 - 12:00
Tue, 2014-11-18 10:00 - 12:00
Tue, 2014-11-25 10:00 - 12:00
Tue, 2014-12-02 10:00 - 12:00
Tue, 2014-12-09 10:00 - 12:00
Tue, 2014-12-16 10:00 - 12:00
Tue, 2015-01-06 10:00 - 12:00
Tue, 2015-01-13 10:00 - 12:00
Tue, 2015-01-20 10:00 - 12:00
Tue, 2015-01-27 10:00 - 12:00
Tue, 2015-02-03 10:00 - 12:00
Tue, 2015-02-10 10:00 - 12:00
Wed, 2014-10-15 10:00 - 12:00
Wed, 2014-10-22 10:00 - 12:00
Wed, 2014-10-29 10:00 - 12:00
Wed, 2014-11-05 10:00 - 12:00
Wed, 2014-11-12 10:00 - 12:00
Wed, 2014-11-19 10:00 - 12:00
Wed, 2014-11-26 10:00 - 12:00
Wed, 2014-12-03 10:00 - 12:00
Wed, 2014-12-10 10:00 - 12:00
Wed, 2014-12-17 10:00 - 12:00
Wed, 2015-01-07 10:00 - 12:00
Wed, 2015-01-14 10:00 - 12:00
Wed, 2015-01-21 10:00 - 12:00
Wed, 2015-01-28 10:00 - 12:00
Wed, 2015-02-04 10:00 - 12:00
Wed, 2015-02-11 10:00 - 12:00
Klausur