Course Announcement - Spring 2022

Math 270: Gröbner Bases and Convex Polytopes

Instructor: Bernd Sturmfels

Contact: bernd at math, 925 Evans
Office hours: below, or by appointment

Lectures: Tuesdays and Thursdays, 9:40-11:00

First Day of Lectures: Tuesday, January 18.
Lectures via Zoom. Contact me for access.
Last Day of Lectures: Thursday, March 3.

Two more in-person discussion sessions:
Monday, February 21, 10-12 in Evans 891
Wednesday, March 2, 10-12 in Evans 891

Prerequisites: Mathematical maturity of an advanced graduate student.
Some Combinatorics, Commutative Algebra and Algebraic Geometry.

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.

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.