__Research Interests__

__Research Interests__

My research interests lie in Commutative Algebra. I study commutative rings which are Noetherian. My dissertation was directed towards developing a tool for approaching Berger's Conjecture which deals with the torsion of the module of Kähler differentials.

I have also spent some time thinking about the following topics:- Hilbert-Samuel multiplicities of flat couples of local rings.
- Homological Algebra, specifically support of Local Cohomology questions.
- Trace Ideals and Reflexive Modules over dimension one non-normal local rings.

__Publications and Preprints__

__Publications and Preprints__

*Valuations and Nonzero Torsion in Module of Differentials*, with Vivek Mukundan (Submitted); arXiv version

*Partial Trace Ideals, Torsion and Canonical Module*(Submitted); arXiv version

*PhD Thesis: Partial Trace Ideals, The Conductor and Berger's Conjecture*

*Torsion in Differentials and Berger's Conjecture*, with Craig Huneke and Vivek Mukundan; Res Math Sci 8, 60 (2021); arXiv version

*Traceable PRFs: Full Collusion Resistance and Active Security*, with D. Wu;

**PKC 2022**; ePrint Archive

*RandomPoints Package for Macaulay2*, with Sankhaneel Bisui, Thái Thành Nguŷen, Zhan Jiang and Karl Schwede (Submitted); arXiv version

*On Reflexive and I-Ulrich Modules Over Curve Singularities*, with Hailong Dao and Prashanth Sridhar; to appear in Transactions of the American Mathematical Society; arXiv version

*Partial Trace Ideals and Berger's Conjecture*; Journal of Algebra, 598: 1–23, 2022; arXiv version

__Talks And Poster__

__Talks And Poster__

__Software __

__Software__

*RandomRationalPoints*, with Sankhaneel Bisui, Thái Thành Nguŷen, Zhan Jiang and Karl Schwede.

A package on Macaulay 2 for computing a random point in a given variety over a finite field.

*SwitchingFields*, with Zhan Jiang.

A package on Macaulay 2 for switching base fields and obtaining natural maps.