Abstract:
The closure of a linear subspace of \(\mathbb C^n\) in an \(n\)-fold product of \(\mathbb{CP}^1\) was first studied by Ardila and Boocher, who showed that the algebraic invariants of this closure beautifully reflect matroid combinatorics. This construction was later used by Huh and Wang to prove the top-heavy conjecture for realizable matroids and is central in the development of Kazhdan-Lusztig theory for matroids. This recent activity was inspired by an analogy with Schubert varieties, so this construction is sometimes referred to as a matroid Schubert variety.
I'll introduce matroid Schubert varieties and then share two results. The first characterizes matroid Schubert varieties as the class of equivariant compactifications of complex vector spaces which have certain properties. The second gives a generalized construction and proves that it also has one of the key properties of matroid Schubert varieties.
Joint work with Connor Simpson and Botong Wang.
Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10.
Join Zoom Meeting: https://washington.zoom.us/j/
Meeting ID: 915 4733 5974