History: Check out the
ten original lectures from December 1994
that led to the book we study.
Description:
This 2-unit course is offered under the header Hot Topics in Mathematics.
It offers an
introduction to Toric Geometry from
the perspective of
combinatorics and
computation. We will
cover
my small book with the same title, with a view towards
recent developments in the field.
Course Text: Gröbner Bases and Convex Polytopes, American Mathematical Society, 1996.
Format: The course consists of 14 lectures,
one for each of the chapters in the book.
Participants are encouraged
to form study groups, work out problems, and collaborate.
Grading:
Students will write a term paper related
to this course.
Inspiration comes from
sources that cite the book.
Contents and format are flexible:
you set your own standards.
DAILY SCHEDULE:
January 18: Gröbner Basics
January 20: The State Polytope
January 25: Variation of Term Orders
January 27: Toric Ideals
February 1: Enumeration, Sampling and Integer Programming
February 3: Primitive Partition Identities
February 8: Universal Gröbner Bases
February 10: Regular Triangulations
February 15: The Second Hypersimplex
February 17: Toric Hilbert Schemes
February 22: Khovanskii Bases
February 24: A Pinch of Commutative Algebra
March 1: Toric Varieties in Algebraic Geometry
March 3: Some Nice Gröbner Bases
More On-Line: There will be
zoom meetings in March and April
for you to discuss your paper.