Research

The Jacobian of a regular orthogonal matroid and torsor structures on spanning quasi-trees of ribbon graphs

With Matthew Baker and Changxin Ding. Adv. Math., 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 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 Orthogonal matroids over tracts. We define antisymmetric matroids, which capture common properties of non-orientable ribbon graphs and the symplectic Grassmannian SpGr(n,2n), and develop the theory of antisymmetric matroids with coefficients.

Orthogonal matroids over tracts

With Tong Jin. Forum Math. Sigma, August 2025. DOI: 10.1017/fms.2025.10085, arXiv: 2303.05353.

We extend the theory of matroids with coefficients, introduced by Dress and Wenzel and developed by Baker and Bowler, to orthogonal matroids, also known as even delta-matroids.