Research

I am interested in combinatorial algebraic geometry and tropical geometry.

Combinatorial Algebraic Geometry: I am working on the generalization of the fruitful compactification system on hyperplane arrangement.

Keywords: Wonderful, tropical and toric compactification; matroid; nested set complex and Bergman complex; matroid Chow ring.

Tropical Geometry: I am working on the classification of an important class of tropical cycles: regular tropical cycles.

Keywords: Tropical complete intersection; matroid; Mixed volume.

Publications & Preprints:

1. Tropical fans supporting a reduced 0-dimensional complete intersection (arXiv).

2. Toward a classification of Tropical complete intersection number one (arXiv) (under review).

Current work:

I am interested in the relationship between wonderful compactifications and tropical compactifications of hyperplane arrangements. Here is a preliminary note/draft (click here for the whole note). This draft serves as a preliminary engine for the current joint work between Fink and me, and I expect to develop it into a paper in the next few weeks.

Comments, suggestions, and related connections are very welcome!