hopf algebras
san francisco state university
universidad de los andes
federico ardila

. hopf cafe . homework . lectures . people . projects . syllabus . texts .

O some comments

Below are the lecture notes and videos for the 2012 Hopf Algebras in Combinatorics class, which I am teaching jointly at San Francisco State University (USA) and the Universidad de Los Andes (Colombia).
I was a bit hesitant to post all of this for anyone to see. Everyone makes mistakes when they teach, but not everyone immortalizes them on the internet. :) But I decided the lectures might be useful to people so I posted them anyway. If they have been helpful to you, please let me know how you are using them - drop me an email to federico at math dot sfsu dot edu. This may help me to improve them in the future.
* An important request *: please either stream the lectures from stream.sfsu.edu or download them only one at a time - our server can't handle it otherwise!

O lecture index

I am SUPER SUPER grateful to Sara Billey for preparing a wonderful index of the lectures, including mini-summaries of each lecture. You can see it here.

O lecture videos

Here you can download the most recent lectures. I will post them as they become available. The videos below require a realmedia player. (Thanks to Arek Goetz!) (They can also be streamed using the latest version of RealPlayer, by typing the address of the file into the player. We will set up a more straightforward streaming link soon.)

lecture video 1 (1.24.12)
lecture video 2 (1.26.12)
lecture video 3 (1.31.12) An error I made is fixed here. Gracias, Yiby!
lecture video 4 (2.02.12)
The videos for Lectures 5-8 are available here. They are unusually large files.
The video for Lecture 9 did not record, I'm very sorry!!!
lecture video 10 (2.23.12)
(In the first five minutes you cannot see what I wrote. The board is just showing the commutative diagram of the antipode, which is on pg 37 here.)
lecture video 11 (2.28.12)
lecture video 12 (3.01.12)
lecture video 13 (3.06.12)
lecture video 14 (3.08.12)
lecture video 15 (3.13.12)
lecture video 16 (3.15.12)
lecture video 17 (3.27.12)
lecture video 18 (4.29.12)
lecture video 19 (4.03.12)
lecture video 20 (4.05.12)
lecture video 21 (4.10.12)
lecture video 22 (4.12.12)
lecture video 23 (4.17.12)
lecture video 24 (4.19.12)
lecture video 25 (4.24.12)
lecture video 26 (4.26.12)
lecture video 27 (5.01.12)
lecture video 28 (5.03.12)
lecture video 29 (5.08.12)
lecture video 30 (5.10.12)

O lecture notes

These are the lecture notes for Lectures 1-9.
If you had downloaded the earlier versions, I have made some (minor) updates.
Lectures 10-11.
Lecture 12.
Lecture 13.
Lectures 14-15.
Lecture 16.
Lectures 17-19.
Lecture 20.
Lecture 21.
Lecture 22.
Lecture 23.
Lecture 24.
Lecture 25.
Lecture 26.
Lecture 27.
Lecture 28.
Lectures 29-30.

At Brian's (and others') request:
If H is simultaneously an algebra and coalgebra, and you want to check that H is a bialgebra, you need to check that these 4 diagrams commute.

Note. As in any lecture or text, there may be occasional mistakes in what I said or wrote. If you notice a significant mistake, please let me know.