Congratulations to all of the winners of the 2022 Fields Medal! The only one I know personally, and whose work I have studied in detail, is June Huh.

I’m happy both for June himself and for the field of combinatorics more broadly, which at one point was not taken seriously enough by the mathematics community to merit Fields Medal level consideration. I’m particularly interested in connections between combinatorics and algebraic geometry, and that is certainly something that June’s work has taken to new heights.

I thought it might be useful for me to post links to my previous blog posts about June’s work here, along with some related links.

Previous blog posts:

- Hodge Theory in Combinatorics
- Whitney Encounters of the Second Kind (Note: the Dowling-Wilson Top-Heavy Conjecture which I refer to in this post was subsequently proved in full generality by Huh and his coauthors; this achievement was cited in Huh’s Fields Medal citation.)
- Lorentzian Polynomials, Part I
- Lorentzian Polynomials, Part II

Here are some related things I’ve written myself:

- Course notes on matroid theory (Lectures 27 through 29 concern Hodge Theory for Matroids)
- My Bulletin of the AMS survey article on the work of Adiprasito-Huh-Katz

Here’s a Quanta Magazine article (published today) which talks about June’s life and work. (I am quoted a couple of times in the article and helped write and copy edit some of the more technical parts)

And here are some survey papers about June Huh’s work from the 2022 Fields Medal website:

- Popular scientific exposition by Andrei Okounkov
- More technical laudatio by Gil Kalai
- June Huh’s own contribution to the 2022 ICM Proceedings

And finally, here is a wonderful 6-minute video in which June Huh talks about his life and his view of mathematics:

A great day for algebraic combinatorics indeed!

Do you plan on publishing these lecture notes on matroid theory?

I’m hoping to, but they need a lot of polishing so it will take a while.