Class Notes

Hello everyone, I TeX’d up a bunch of notes from the lectures and lecture notes and thought others might be interested in getting a copy of them. Use with caution – these notes are not complete and there may be errors (particularly when Federico posted corrections after the fact). You can find the PDF at the following link:

If anyone wants the TeX files I can provide those as well.


About juliaudell

My research interests consist primarily of bioinformatics. Currently I'm trying to find structure in gene sequencing data for a highly variable and mysterious gene that plays a major role in the immune system. I have a soft spot for combinatorics and I love finding new and interesting applications of it in the world around us. When I'm not working or studying, I can be found listening to music while playing in the garden or kitchen. I love trying flavorful new recipes so send your favorites my way.


    • Have you considered using these notes as a starting point for a book on Hopf algebras from a combinatorial perspective?

      • This question would be better directed towards Federico – the notes are half summaries of the first third of the course and transcripts of the lectures from the second two thirds. This represents his academic effort, not mine.

        I have actually considered doing some writing on various bits in advanced mathematics that I think are quite accessible to a general audience, Hopf algebras included, but the fact is that my background in algebra isn’t very robust and I won’t be taking many courses in it in the future. It’ll take me a very long time to digest this kind of material outside a course in order to be able to write on it, I’m afraid, but it’s still a long-term goal.

  1. First paragraph: Of course. What I meant (implicitly) was whether you have brought up the idea to Federico. After all, he also directly referred to other works throughout his notes –to the best of my knowledge, he followed Sweedler, Schmitt, Rota and others to come up with his notes. He could have even followed some of the work by Aguiar. Part of his academic effort was to put several of these sources together to present one coherent picture of Hopf algebras in combinatorics.

    In any case, it would be nice to see a single book that provides an introduction to Hopf algebras from a combinatorial perspective. Based on what I have heard from some people, it seems that such a book does not exist.

  2. Note – The document’s header read something like “850 definitions”, which is pretty misleading. I edited it to be more descriptive and give credit to our wonderful professor. (Grades are due in a few weeks and what can I say, I have an entire thesaurus of synonyms for “wonderful” packed up and ready to go.)

    I agree that a basic text on the subject would be wonderful. If it existed as a book I’d buy 10 copies and give them out as Christmas presents.

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