__Research Interests__

__Research Interests__

My research interests lie in Commutative Algebra. My dissertation and also quite a bit of subsequent work has been directed towards developing a tool for approaching Berger's Conjecture which deals with the torsion of the module of Kähler differentials. Even though, some partial progress was made, the question is still wide open.

I have also spent some time thinking about the following topics:- Hilbert-Samuel multiplicities of flat couples of local rings.
- Numerical semigroup rings
- Trace Ideals and Reflexive Modules over dimension one non-normal local rings.
- Injective curvature of modules.

__Publications and Preprints__

__Publications and Preprints__

*Two Criteria for Quasihomogeneity*, with Vivek Mukundan; To appear in the Proc. Amer. Math. Soc.

*Extremal behavior of reduced type of one dimensional rings*, with Vivek Mukundan (Submitted); arXiv version

*Valuations and Nonzero Torsion in Module of Differentials*, with Vivek Mukundan; Bulletin des Sciences Mathématiques, Volume 187, October 2023, 103287 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

*Finding Points On Varieties with MACAULAY2*, with Sankhaneel Bisui, Thái Thành Nguŷen, Zhan Jiang and Karl Schwede (Journal of Software for Algebra and Geometry, Vol 13 (2023) 33-43); arXiv version

*On Reflexive and I-Ulrich Modules Over Curve Singularities*, with Hailong Dao and Prashanth Sridhar; Trans. Amer. Math. Soc. Ser. B 10 (2023), 355-380; 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.