19039
Lecture
WiSe 12/13: Diskrete Geometrie I
Raman Sanyal
Comments
Inhalt This is the first in a series of three courses on discrete geometry. The aimof the course is a skillful handling of discrete geometric structuresincluding analysis and proof techniques. The material will be a selection ofthe 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-)conjectureGeometry of linear programming - linear programs, simplex algorithm, LP-dualityCombinatorial geometry / Geometric combinatorics - Arrangements of points and lines, Sylvester-Gallai, Erdos-Szekeres, - Szemeredi--Trotter - Arrangements, zonotopes, zonotopal tilings, oriented matroidsExamples, examples, examples - regular polytopes, centrally symmetric polytopes - extremal polytopes, cyclic/neighborly polytopes, stacked polytopes - combinatorial optimization and 0/1-Polytope Zielgruppe For students with an interest in discrete mathematics and geometry, this isthe starting point to specialize in discrete geometry. The topics addressed inthe course supplement and deepen the understanding for discrete-geometricstructures appearing in differential geometry, topology, combinatorics, andalgebraic geometry. Voraussetzungen Solid background in linear algebra.Knowledge in combinatorics and geometry is advantageous. Literatur - G.M. Ziegler "Lectures on Polytopes" - J. Matousek "Lectures on Discrete Geometry"Further literature will be announced in class. close
32 Class schedule
Additional appointments
Wed, 2013-04-10 14:00 - 16:00Regular appointments
Tue, 2012-10-16 16:00 - 18:00
Tue, 2012-10-23 16:00 - 18:00
Tue, 2012-10-30 16:00 - 18:00
Tue, 2012-11-06 16:00 - 18:00
Tue, 2012-11-13 16:00 - 18:00
Tue, 2012-11-20 16:00 - 18:00
Tue, 2012-11-27 16:00 - 18:00
Tue, 2012-12-04 16:00 - 18:00
Tue, 2012-12-11 16:00 - 18:00
Tue, 2012-12-18 16:00 - 18:00
Tue, 2013-01-08 16:00 - 18:00
Tue, 2013-01-15 16:00 - 18:00
Tue, 2013-01-22 16:00 - 18:00
Tue, 2013-01-29 16:00 - 18:00
Tue, 2013-02-05 16:00 - 18:00
Tue, 2013-02-12 16:00 - 18:00
Wed, 2012-10-17 10:00 - 12:00
Wed, 2012-10-24 10:00 - 12:00
Wed, 2012-10-31 10:00 - 12:00
Wed, 2012-11-07 10:00 - 12:00
Wed, 2012-11-14 10:00 - 12:00
Wed, 2012-11-21 10:00 - 12:00
Wed, 2012-11-28 10:00 - 12:00
Wed, 2012-12-05 10:00 - 12:00
Wed, 2012-12-12 10:00 - 12:00
Wed, 2012-12-19 10:00 - 12:00
Wed, 2013-01-09 10:00 - 12:00
Wed, 2013-01-16 10:00 - 12:00
Wed, 2013-01-23 10:00 - 12:00
Wed, 2013-01-30 10:00 - 12:00
Wed, 2013-02-06 10:00 - 12:00
Wed, 2013-02-13 10:00 - 12:00