My work falls into both landscapes of algebraic geometry and commutative algebra where I utilize the machinery of derived categories to understand problems lying within these two subject matters. This direction of research has interactions with singularity theory, and in essence the objective is to understand the behavior through homological methods coming from derived categories. Broadly speaking, I am interested in problems regarding the applications of derived categories in algebraic geometry and commutative algebra.

Papers

“Descent conditions for strong generation in derived categories” arxiv version, submitted.

“Strong generation and (co)ghost index in module categories” joint with Souvik Dey and Ryo Takahashi- arxiv version.

“High Frobenius Pushforwards generate the bounded derived category” joint work w/ Matthew Ballard, Srikanth B. Iyengar, Alapan Mukhopadhyay, and Josh Pollitz - arxiv version, submitted.

“Intrinsic Curvature For Schemes.” M.Sc. thesis (2020).

Talks (last two years)

Algebraic Geometry seminar, University of Georgia, October 2023

Syzygies and mirror symmetry worskhop, American Institute of Mathematics, September 2023

New Directions in Group Theory and Triangulated Categories, May 2023

Georgia Algebraic Geometry Symposium, University of Georgia, May 2023

Categorical methods in moduli theory, University of Pennsylvania, April 2023

AMS Special Session on Interactions between Noncommutative Ring Theory and Algebraic Geometry, Spring Central Sectional, April 2023

AMS Special Session on Recent Developments in Commutative Algebra, Southeast Sectional, March 2023

Algebraic Geometry seminar, University of Utah, September 2022

Algebraic Geometry & Singularity theory workshop, University of Washington, June 2022