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 particular
exploting techniques from noncommutative algebra. 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 monomial ideals
that are derived via certain operations from matroid
complexes and well as a notion of higher crosscut
complexes.
On a Generalization of Ulrich Modules and its
Applications (with Ela Celikbas, Olgur Celikbas, Ryo
Takahashi, and Yongwei Yao). (accepted to Tohoku Math
Journal) 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.
Exterior Powers and
Tor-persistence (with Jonathan Montaño and Keri
Sather-Wagstaff). Journal
of Pure and Applied Algebra. 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.
Higher Nerves of Simplicial Complexes
(with Hailong Dao, Joseph Doolittle, Ken Duna, Bennet
Goeckner, and Brent Holmes). Algebraic
Combinatorics. arXiv Link.
Hom and Ext, Revisited (with Hailong Dao and Mohammad
Eghbali). Journal
of Algebra. arXiv Link.
Ordinary and Symbolic Powers of Matroids via Polarization (with Paolo Mantero)
Annihilators of (co)Homology and Their Influence on the Trace Ideal (with Sarasij Maitra). 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.
Behavior of (co)Homology for Rings with Small Numerical Properties (with Sarasij Maitra)
On the Depth of Tensor Products and Auslander Bounds (with Andrew Soto-Levins)
Centers of Endomorphism Rings and Reflexivity (with Souvik Dey)
*: This means some version exists but has not yet been made available to the public.
