Math 676: Numerical Algebraic Geometry
Fall 2012
Time/place: T/H 2:00–3:15 p.m. in Engineering E104
Course website: www.math.colostate.edu/∼bates/courses/F12/676
Text: None required, though I will be following Sommese & Wampler for the first few weeks. Links
to useful technical articles will be posted on the website, and I’ll share fresh copies of the upcoming
Bertini/NAG book as they become available.
Instructor info: Prof. Dan Bates, bates@math.colostate.edu, Weber 221 (1-1037)
Office hours for 560: None.
Prerequisites: Calculus and linear algebra. Many other fields come into play, but I can’t well
require them all. If you are missing background on some topic, let me know and we’ll fill it in one
way or another.
Topics to be covered: We will hit all of the basic ideas of numerical algebraic geometry (algebra/geometry of polynomial systems, homotopy continuation, witness sets, methods for computing
and manipulating witness sets, etc.) and many advanced topics. By the end of the course, you will
know how to use both the methods and the software of numerical algebraic geometry, and you will
know of several open problems that might lead to original research for you.
Structure of the class: The course has three main components: basic ideas, recent advances, and
independent study. In the first part (lasting 5-ish weeks), I’ll be filling you in on basic ideas. Please
ask questions!! While I can (and unfortunately often do) revert to regular old park & blow lectures,
I’d really like to have an active dialogue in this class, as appropriate. Once you are beginning to
feel comfortable with the ideas and software (which I’ll demonstrate), you should start posing your
own problems (one your own or in small groups) and playing around with the software and ideas.
After we are done going over the basic ideas, we’ll start digging into some hot topics (recently
closed ones, current ones, and upcoming ones). We’ll typically use technical papers as our source
for this material. I will also plan to hit a bunch of applications during this part of the course.
Throughout the course, I am happy to fit in time for people to give talks about NAG-related
topics or experiments, whether they are fully completed or ongoing. In fact, such experiments and
independent study should help to spark dialogue and might lead to more experiments. My students
should plan to talk a bit about their own work, and I encourage anyone who has anything to say
to let me know ASAP that you’d like to say something in class. I’ll be more than happy to work
you into the schedule.
The work load for this class is admittedly ill-determined. I would like everybody to at least do some
reading and experiment with the software. I would also like everybody to come to class regularly
and participate from time to time. I expect everybody to give a talk, even a really brief one, at
some point.
Grading: This is a topics course, so grading should be fairly clear. If you participate and give a
talk (even a really brief one), you’ll get an A. Minimal participation/attendance and/or no talk
will result in a lower grade. For the sake of being clear, let’s say participation is 50% of your grade
and the talk is 50% of your grade.
Feedback: I am always happy to hear it, even if it is negative. I am happy to adapt my teaching
style a bit if it will make the course work better for you.
Final Note: You should know that I have insulin-dependent diabetes and may therefore need to
sit down and take it easy occasionally. There is also the very slight risk that I could have very low
blood sugar at some point, causing me to pass out. If that happens (the probability of this is very
low), I will need somebody to call 911. Please don’t worry: I haven’t passed out yet and don’t
intend to! Even if I do pass out, I am not in any significant danger.