Solid background in linear algebra. Knowledge in combinatorics and geometry is advantageous.
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 ... read more
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:
polyhedra and polyhedral complexes
configurations of points, hyperplanes, subspaces
Subdivisions and triangulations (including Delaunay and Voronoi)
Representations and the theorem of Minkowski-Weyl
polarity, simple/simplicial polytopes
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
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.