MA 714, Geometric Combinatorics.
This is
a topics course,
or more accurately,
a collection of hor-d'oeuvres
from the broad area
of Geometric Combinatorics.
The collection of topics are taken from
algebra, topology, algebraic geometry
and polytopes
and is based upon a series of graduate courses
given during the Summer 2004 at the
Institute for Advanced Study/Park City.
COURSE OUTLINE
-
Introduction to Hyperplane Arrangements.
-
Introduction to Coxeter Groups and Cluster Algebras
-
Discrete Morse Theory
-
Topological Combinatorics
-
Introduction to Toric Varieties
-
Tropical Geometry
-
Some Convex Geometry (a la Barvinok)
-
Face vectors of 4-polytopes
-
Additional topics, as time permits
PREQUISITE:
There is no formal prerequisite
for this course.
Knowledge of algebra or topology is useful,
but not necessary.
http://www.ms.uky.edu/~readdy/714/Geometric_Combinatorics/