Research

Poster presentation at JMM 2023

Photo courtesy: AWM

My research area is Commutative Algebra. I enjoy looking at algebraic invariants via combinatorial properties. A simplicial complex is an important combinatorial tool for studying properties of squarefree monomial ideals. In the work with my collaborators, we try to characterize some algebraic properties of an ideal in terms of a simplicial complex associated with the ideal. Some themes include the Lefschetz properties of Artinian algebras, linear resolution and Castelnuovo-Mumford regularity of squarefree monomial ideals, vertex decomposability of simplicial complex.

I also like looking at Hilbert function of numerical semigroup rings.

Here is the link to the Graduate Student Algebra Seminar at KU, that I co-organize: Algebra Seminar, KU

Publications and Preprints

1) On the Lefschetz property for quotients by monomial ideals containing squares of variables; joint work with Hailong Dao. Communications in Algebra https://doi.org/10.1080/00927872.2023.2260012 arxiv.org/abs/2112.09434

2) Simplicial complexes with many facets are vertex decomposable; joint work with Anton Dochtermann, Jay Schweig, Adam Van Tuyl, Russ Woodroofe. arxiv.org/abs/2403.07316

3) Regularity of a monomial ideal via its complement ; joint work with Hailong Dao (in preparation).