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Course Announcement - Spring 2022

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Math 270:
Gröbner Bases and Convex Polytopes

**Contact:** bernd at math, 925 Evans

**Office hours:** below, or by appointment

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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.

** 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.