Notes and papers on algebra and algebraic combinatorics


Comments and corrections are welcome on all of these writings! (This includes "trivial" typos. Let me know at A@B.com, where A = darijgrinberg and B = gmail.)
Texts:
Notes taken in lectures:
Papers (publications and preprints):

Published papers don't always appear in the same form below as they appear in the journals. In particular, editorial changes and (on occasion) some judgment calls from referees are not reflected in the preprints downloadable from this page. (However, the preprints sometimes contain more details and occasional post-publication corrections.)
Other writings:
Talk slides not corresponding to papers (mostly expository):
Work supervised:

I have been a mentor in the PRIMES program at MIT from 2012 to 2015. In this function, I have supervised college students doing mathematical research projects; these projects led to the following writings by the students:
Sidenotes to Michiel Hazewinkel: Witt vectors. Part 1:

Witt vectors reside somewhere on the crossroads between algebra, combinatorics and number theory. Hazewinkel's text is, in my opinion, a must-read for everyone interested in at least two of these fields. It also sheds light on the representation theory of symmetric groups, the theory of symmetric polynomials, Hopf algebras and λ-rings.

I tend to advise Hazewinkel's text to anyone interested in any of the subjects mentioned, due to its very vivid and explanatory writing style. (It was the main thing that made me study combinatorial algebra!) Unfortunately, a multitude of typos makes reading it harder than it should be. If you have troubles with understanding something in the text, the reason may be in this list of errata (plus a few remarks). (Here is a more complete collection of errata which I sent to the author; these include obvious spelling mistakes which won't hinder anyone at understanding the text.)
Warning: Don't take my list of errata at face value. They can contain false positives and wrong corrections.

Here are some sidenotes I have made. Usually, these contain proofs of assertions which are mentioned without proof in Hazewinkel's work. Some contain generalizations/extensions (however, it's mostly the cheap kind of generalization, that barely adds any new content). I have written them for myself to keep track of what's true and what isn't; unfortunately they aren't very readable... LaTeX sourcecode of the above.

Sidenotes to Pavel Etingof, Oleg Golberg, Sebastian Hensel, Tiankai Liu, Alex Schwendner, Dmitry Vaintrob, and Elena Yudovina: Introduction to representation theory:

See also my errata and marginalia to various papers, textbooks and notes.
Further plans (outdated):

Algebra notes

Back to the main site

Darij Grinberg