Description: Description: Description: C:\Tai's Documents\public_html\images\write.gifResearch

Last updated: April 2025

The reviews of my published papers can be found on MathSciNet. Copies of manuscripts are on the arXiv.

Research Interest

My research lies at the intersection of commutative algebra, algebraic geometry, and combinatorics, with a focus on algebraic invariant, asymptotic behaviors and combinatorial structures. Particularly, I work on the following topics:
  1. Homological invariants and properties. I am interested in structures of the minimal free resolutions. I also investigate bounds, combinatorial interpretation, and asymptotic behavior of invariants such as the depth and Castelnuovo-Mumford regularity.
  2. Algebraic invariants and combinatorial structures. I examine how algebraic invariants of ideals and graded families of ideals can be understood from graph theory and convex geometry. I look at edge ideals and Stanley ideals of graphs and simplicial complexes, the construction of Newton polyhedra, Newton-Okounkov bodies/regions, and study how combinatorial data and structures govern algebraic properties and invariants of the ideals.
  3. Polynomial interpolation and ideal containment problem. I investigate Chudnovsky's and Demailly's conjectures in the polynomial interpolation problem for several variables. My approach is via the ideal containment. Specifically, I consider stable versions of Harbourne and Harbourne-Huneke containment between symbolic and ordinary powers of ideals.
  4. Algebraic theory of Lojasiewicz exponents. I study Lojasiewicz exponents of pairs of graded families of ideals. My approach is to bring a valuative framework into the study of this singularity invariant.

Collaborators

Students