Broadly, I am interested in applications of derived categories to the study of singularities in commutative algebra and algebraic geometry. More specifically, I'm interested in derived splinters, closure operations, and the McKay correspondence.
Publications
The Briançon-Skoda theorem for pseudo-rational and Du Bois singularities. Submitted. [arXiv]
With Linquan Ma, Rebecca R.G., and Karl Schwede
Here is a recent talk on this paper (as well as the one below) at BIRS in October 2025.
Closure operations induced via resolutions of singularities in characteristic zero. Preprint. [arXiv]
With Neil Epstein, Rebecca R.G., and Karl Schwede
Derived characterizations for rational pairs à la Schwede-Takagi and Kollár-Kovács. Submitted. [arXiv]
With Pat Lank and Sridhar Venkatesh
An explicit derived McKay correspondence for some complex reflection groups of rank two. Under revision. [arXiv]
With Anirban Bhaduri, Yael Davidov, Eleonore Faber, Katrina Honigs, C. Eric Overton-Walker, and Dylan Spence
Homological properties of the relative Frobenius morphism. Proceedings of the AMS (2025). [arXiv] [journal]
Multiplier ideals and klt singularities via (derived) splittings. Mathematical Research Letters (to appear). [arXiv]
Completely controlling the dimensions of formal fiber rings at prime ideals of small height. J. Commut. Algebra (2019). [arXiv] [journal]
With Sarah Fleming, Lena Ji, Susan Loepp, Nina Pande, and David Schwein
Controlling the dimensions of formal fibers of a unique factorization domain at the height one prime ideals. J. Commut. Algebra (2018). [arXiv] [journal]
With Sarah Fleming, Lena Ji, Susan Loepp, Nina Pande, and David Schwein
Generalizing the Minkowski Question Mark Function to a Family of Multidimensional Continued Fractions. International Journal of Number Theory (2018). [arXiv] [journal]
With Tom Garrity