19039
Vorlesung
WiSe 13/14: Diskrete Geometrie I
Günter Ziegler
Zusätzl. Angaben / Voraussetzungen
Solid background in linear algebra. Knowledge in combinatorics and geometry is advantageous.
Kommentar
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, andalgebraic geometry. Schließen
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, andalgebraic geometry. Schließen
Literaturhinweise
32 Termine
Regelmäßige Termine der Lehrveranstaltung
Di, 15.10.2013 10:00 - 12:00
Di, 22.10.2013 10:00 - 12:00
Di, 29.10.2013 10:00 - 12:00
Di, 05.11.2013 10:00 - 12:00
Di, 12.11.2013 10:00 - 12:00
Di, 19.11.2013 10:00 - 12:00
Di, 26.11.2013 10:00 - 12:00
Di, 03.12.2013 10:00 - 12:00
Di, 10.12.2013 10:00 - 12:00
Di, 17.12.2013 10:00 - 12:00
Di, 07.01.2014 10:00 - 12:00
Di, 14.01.2014 10:00 - 12:00
Di, 21.01.2014 10:00 - 12:00
Di, 28.01.2014 10:00 - 12:00
Di, 04.02.2014 10:00 - 12:00
Di, 11.02.2014 10:00 - 12:00
Mi, 16.10.2013 10:00 - 12:00
Diskrete Geometrie I
Mi, 23.10.2013 10:00 - 12:00
Diskrete Geometrie I
Mi, 30.10.2013 10:00 - 12:00
Diskrete Geometrie I
Mi, 06.11.2013 10:00 - 12:00
Diskrete Geometrie I
Mi, 13.11.2013 10:00 - 12:00
Diskrete Geometrie I
Mi, 20.11.2013 10:00 - 12:00
Diskrete Geometrie I
Mi, 27.11.2013 10:00 - 12:00
Diskrete Geometrie I
Mi, 04.12.2013 10:00 - 12:00
Diskrete Geometrie I
Mi, 11.12.2013 10:00 - 12:00
Diskrete Geometrie I
Mi, 18.12.2013 10:00 - 12:00
Diskrete Geometrie I
Mi, 08.01.2014 10:00 - 12:00
Diskrete Geometrie I
Mi, 15.01.2014 10:00 - 12:00
Diskrete Geometrie I
Mi, 22.01.2014 10:00 - 12:00
Diskrete Geometrie I
Mi, 29.01.2014 10:00 - 12:00
Diskrete Geometrie I
Mi, 05.02.2014 10:00 - 12:00
Diskrete Geometrie I
Mi, 12.02.2014 10:00 - 12:00
Diskrete Geometrie I