Toric Varieties Fan Club

This is the page for the Spring 2021 Toric Varieties Fan Club (Reading Group), which is open to all UW Math grad students, but will require a certain amount of participation and work to receive course credit (details below).

Resources

We plan to read Cox, Little, and Schenck's Toric Varieties, which can be downloaded here: [1].

Meeting Schedule

14 weeks total, starting on January 25, adjusting throughout the semester as necessary.

Meetings will be on Mondays and Wednesdays at 1-2:30pm, where the first hour is devoted to reviewing the assigned reading, led by a designated speaker, and the half-hour is used to collaborate on exercises. Meetings will be held virtually using this link: [2].

Optimistic Reading Schedule:

Week 1

Monday, January 25: Ch. 1.0 Background: Affine Varieties   (Speaker: Caitlyn Booms)

Wednesday, January 27: Ch. 1.1 Introduction to Affine Toric Varieties  (Speaker: Ola Sobieska)

September 23

a. Ch. 2: Grobner Bases, Sections 7-8   (Speaker: Colin Crowley)

b. Chapter 2 Exercises

September 30

a. Ch. 3: Elimination Theory, Sections 1-3   (Speaker: Caitlyn Booms)

b. Ch. 3: Elimination Theory, Sections 4-6   (Speaker: Will Hardt)

October 7

a. Ch. 4: The Algebra-Geometry Dictionary, Sections 1-3   (Speaker: Erika Pirnes)

b. Ch. 4: The Algebra-Geometry Dictionary, Sections 4-6   (Speaker: Alex Hof)

October 14

a. Ch. 4: The Algebra-Geometry Dictionary, Sections 7-9   (Speaker: Ivan Aidun)

b. Chapter 3 and 4 Exercises (Led by Maya Banks)

October 21

a. Guest Lecture: Daniel Erman

b. Catch up/Problem Session

October 28

a. Ch. 5: Polynomial and Rational Functions on a Variety, Sections 1-3   (Speaker: Owen Goff)

b. Ch. 5: Polynomial and Rational Functions on a Variety, Sections 4-6   (Speaker: Erika Pirnes)

November 4

a. Ch. 8: Projective Algebraic Geometry, Sections 1-4   (Speaker: John Cobb)

b. Ch. 8: Projective Algebraic Geometry, Sections 5-7   (Speaker: Eiki Norizuki)

November 18

a. Ch. 9: The Dimension of a Variety, Sections 1-3   (Speaker: Lorenzo Najt)

b. Ch. 9: The Dimension of a Variety, Sections 4-6   (Speaker: Maya Banks)

November 25

a. Chapter 5, 8, and 9 Exercises

b. Chapter 5, 8, and 9 Exercises

General Meeting Structure

This reading group will be structured as follows. Every meeting will have an assigned speaker, who will usually be one of the reading group participants, but could at times be an older grad student or professor. It will be expected that everyone attending will read the assigned sections prior to the meeting. The speaker is expected to additionally work out some examples prior and will be responsible for lecturing on the reading material and guiding the group discussion during the meeting. The schedule will be pretty flexible and will be adjusted throughout the semester. Daniel Erman will be our faculty advisor, and in order to receive credit (up to 3 credits), participants will be expected to attend all meetings, be the speaker twice, and do several exercises. We will also use Macaulay2 during the exercise sessions to get comfortable both computing examples by hand and by using a computer.

If you are interested in joining this reading group or have any questions, please contact Caitlyn Booms at cbooms@wisc.edu by Sept. 4, 2019.