Mathematical Gemstones
Young tableaux are to planes as labeled trees are to curves. Continuing from the previous post in this series, we introduce the Chow ring of $\overline{M}_{0,n}$ and some important classes. Recall that in the first post, we answered the question “How many cubic curves in $\mathbb{P}^3$ pass...
Mathematical Gemstones
Young tableaux are to planes as labeled trees are to curves. Continuing from the previous post in this series, we now show how to think of $\overline{M}_{0,n}$ as a projective variety. We now show how to look from the perspective of a single point, and combine this with the forgetting maps, to...
Mathematical Gemstones
Young tableaux are to planes as labeled trees are to curves. Continuing from the motivation of the previous post, we now dive into the structure of the moduli space $\overline{M}_{0,n}$, and construct two recursive structures that lead to beautiful inductive theory, and, in the next post, the...
Mathematical Gemstones
I haven’t posted in a while; it’s time to dust off this blog and get things started again with a guest post! In this post, guest user Anon1 posted a proof of the existence of finite fields of every possible order. Today I’ll share a writeup by the same user on the Schur-Zassenhaus Theorem in...
Mathematical Gemstones
In this arXiv paper, Hikita recently posted a proof of the famous Stanley-Stembridge conjecture! I went through the proof with my Advanced Combinatorics class, and wrote up lecture notes here: Lecture Notes on Stanley-Stembridge Part I Lecture Notes on Stanley-Stembridge Part II which I will...
Mathematical Gemstones
I have written about the flag variety, the Springer resolution, and the relation between the type A Springer correspondence and Hall-Littlewood polynomials in a previous sequence of posts. Time to extend this construction to the (type A) affine flag variety, corresponding to affine Lie type...