About This Class

URL: http://drorbn.net/21-1350 and/or http://www.math.toronto.edu/~drorbn/classes/21-1350-KnotTheory.

Disclaimer. Everything on this page remains tentative until it had happenned. The Evil Virus situation may force us to make last minute changes to anything.

Agenda. Find a poly-time-computable strong knot invariant with good algebraic properties.

Abstract. The destination will be "a poly-time computable strong knot invariant with good algebraic properties". But you will be taking the course for the journey, not for the destination: What are knots and what are some of the problems around them? Why care about "invariants with good algebraic properties"? What is the "Yang-Baxter equation"? What are "virtual tangles"? What are "Hopf algebras"? Why would a topologist care about computations in Heisenberg algebras more than most physicists? How does Gaussian integration, and how do Feynman diagrams, arise in pure algebra? What is the "Drinfel'd Double Procedure"? Are we there yet?

The professor for this class does not believe anything that he does unless it is coded and the code runs. A useful life skill you will learn here is that even the incredibly abstract can become a computer program, often with no loss to its beauty.

Even more details are here.

Instructor. Dror Bar-Natan, drorbn@math.toronto.edu (for course administration matters only; math on email is slow and prone to misunderstandings, so I generally avoid it). Office: Bahen 6178.

Classes. Mondays and Wednesdays at 3-4PM and Fridays at 1-2PM, at Bahen 6178. A complete video record will be available here, at a few hours delay.

Office Hours. Tuesdays at 9:30-10:30 at Bahen 6178 and online at http://drorbn.net/vchat.

Texts. No "course text"! But maybe one day I will write a text following this course...

Prerequisites. The core classes in topology and in algebra, or the willingness and ability to learn the relevant background material from these classes on the fly.

Marking Scheme. About 10 HW equal-weight assignments, only the top 7 will count.

Homework. Assignments will be posted on the course web page (usually on Wednesdays) approximately on the weeks shown in the class timeline.

Photo Album. Just for fun, I will maintain a public photo album related to MAT1350. Please send me photos! You may send your own portrait or any other photo of you or other students engaging in MAT1350-related activities. You may overlay your photos with some caption text, if you wish. If your photos contain images or names of any persons other than youself you must obtain permission from these people before you submit their photos, and when you submit, you must CC all people seen or mentioned in the photos. If anybody will ever ask me to remove a photo in which they appear or are mentioned, I will do so ASAP with no questions asked.

Accessibility Needs. The University of Toronto is committed to accessibility. If you require accommodations for a disability, or have any accessibility concerns about the course, the classroom or course materials, please contact Accessibility Services as soon as possible.