Office: MSB M312 Phone: (860)
486-3850 e-mail: kaufmann@math.uconn.edu
Office hours: TuTh
Topics in Geometry and Topology
I
TuTh TuTh
Syllabus
Short description: Toric varieties
are a class of examples of varieties
(complex algebraic manifolds) which have two main attractive features:
(1)
They
appear in many contexts, such as Codes, Algebraic
Geometry, Symplectic Geometry, Number
theory, String
Theory, Combinatorics, Singularity theory,
and
numerous other contexts.
(2)
Everything
is calculable in terms of combinatorial data. So
they give concrete examples to many geometric concepts.
It can be said that toric
varieties are the tool of choice today for many fields in mathematics.
Close to
my heart is mirror symmetry and string theory, which makes heavy use of
toric geometry. But they are of equal
importance in
classical geometry and number theory. Since they are described by
combinatorial
data, all the abstract concepts can be presented in detailed concrete
calculations. This helps one (a) to understand the concepts and (b) to
actually
prove theorems by calculations.
Audience: Graduates with basic knowledge about topology,
geometry
and algebra.
Textbook: I will
probably use
more than one source, but the main source will be:
Introduction to Toric Varieties by William Fulton.
News: Final is available! Please mail to me by the
date indicated. Good luck and thanks.
Homework