Research

My research is in commutative algebra and algebraic combinatorics. On the commutative algebra side, my interests include (but are not limited to) questions about depth, multiplicities and measures of singularity, Cohen-Macaulay representation theory, and  derived categories. I have been working recently on trace ideals/submodules, Gorenstein properties of DG algebras, and homological rigidity conjectures such as the Auslander-Reiten conjecture, in particular exploiting 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.

Published/Accepted Papers:

         
           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.

Preprints:

G-levels of perfect complexes (with Lars Winther Christensen, Antonia Kekkou, and Andrew Soto Levins). arXiv Link.
On the depth of tensor products over Cohen-Macaulay Rings (with Kaito Kimura and Andrew Soto Levins). arXiv Link.
Ordinary and symbolic powers of matroids via polarization (with Paolo Mantero). arXiv Link.
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 self tensor products. arXiv Link.

Preliminary Preprints*:

  Centers of Endomorphism Rings and Reflexivity (with Souvik Dey)
 

*: This means some version exists but has not yet been made available to the public.