Selected Papers

• The Jacobian of a regular orthogonal matroid and torsor structures on spanning quasi-trees of ribbon graphs (with Matthew Baker and Changxin Ding), arXiv: 2501.08796, 2025.

We show that the set of spanning quasi-trees of a ribbon graph inherits a group structure from its Jacobian group (which was first introduced by Merino, Moffatt, and Noble) without the distinguished identity element. It extends the same results for plane graphs by Chan–Church–Grochow and Baker–Wang, casting light on the role of embeddings of graphs.

A generalized Farkas Lemma for oriented orthogonal matroids is proved and used as a key lemma. It follows from the signed circuit axiom of oriented orthogonal matroids, as established in “Orthogonal matroids over tracts.”

• Baker-Bowler theory for Lagrangian Grassmannians, Int. Math. Res. Not. IMRN, April 2025. DOI: 10.1093/imrn/rnaf094, arXiv: 2403.02356.

This is a sequel of the paper “Orthogonal matroids over tracts.” We define a new combinatorial object, named antisymmetric matroids, which captures common properties of (non-orientable) ribbon graphs and symplectic Grassmannian SpGr(n,2n), and develop theory of antisymmetric matroids with coefficients. Also, antisymmetric matroids are closely related with delta-matroids and gaussoids.

* At first, I named it a sympletic matroid, but since this name was already used in Coxeter matroid theory, I decided to name it antisymmetric matroid instead.

• Orthogonal matroids over tracts (with Tong Jin), arXiv: 2303.05353, 2023.

We extend theory of matroids with coefficients, introduced by Dress and Wenzel and developed by Baker and Bowler, to orthogonal matroids (= even delta-matroids). Orthogonal matroids are combinatorial data related to (orientable) ribbon graphs and orthogonal Grassmannian OGr(n,2n).