My research is in commutative algebra
and algebraic combinatorics. On the commutative algebra
side, my interests include questions about depth,
multiplicities and measures of singularity, Cohen-Macaulay
representation theory, and prime characteristic methods. I
have been working recently on tensor products over
endomorphism rings, on a notion of generalized trace
submodules, and on homological rigidity conjectures such
as the Auslander-Reiten conjecture. In algebraic
combinatorics, I am interested in Stanley-Reisner theory
and understanding certain homological conditions, such as
bounds on depth or Serre conditions, from the simplicial
complex perspective. I have been working recently on
studying certain monomial ideals that are derived via
certain operatons from matroid complexes and well as a
notion of higher crosscut complexes and connections to
higher nerves.
Hom and Ext, Revisited (with Hailong Dao
and Mohammad Eghbali). Journal
of Algebra. arXiv Link.
Higher Nerves of Simplicial Complexes (with
Hailong Dao, Joseph Doolittle, Ken Duna, Bennet Goeckner,
and Brent Holmes). Algebraic
Combinatorics. arXiv Link.
Maximal Cohen-Macaulay Modules That Are Not
Locally Free on the Punctured Spectrum (with Toshinori
Kobayashi and Ryo Takahashi). Journal
of Pure and Applied Algebra. arXiv Link
Rank Selection and Depth Conditions for
Balanced Simplicial Complexes (with Brent Holmes). Electronic
Journal of Combinatorics. arXiv Link.
Minimal Cohen-Macaulay Simplicial Complexes
(with Hailong Dao and Joseph Doolittle). SIAM
Journal on Discrete Mathematics. arXiv Link.
Extremal Growth of Betti Numbers and
Trivial Vanishing of (Co)homology (with Jonathan Montaño).
Transactions
of the AMS. arXiv Link.
Exterior Powers and Tor-persistence (with
Jonathan Montaño and Keri Sather-Wagstaff). Journal
of Pure and Applied Algebra. arXiv Link.
Generalized Trace Submodules and Centers of Endomorphism Rings. arXiv Link.
On the Vanishing of Ext Modules Over a Local Unique Factorization Domain with an Isolated Singularity (with Kaito Kimura, Yuya Otake, and Ryo Takahashi). arXiv Link.
Endomorphism Algebras Over Commutative Rings and Torsion in Tensor Products. arXiv Link.
On a Generalization of Ulrich Modules and its Applications (with Ela Celikbas, Olgur Celikbas, Ryo Takahashi, and Yongwei Yao). arXiv Link.
Polarizations, Symbolic Powers, and Matroids (with Paolo Mantero)
*: This means some version exists but has not yet been made available to the public.
