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.
During my PhD, I also was engaged in reading and reasearching various topics in Cryptography with
Prof. David Wu.
arXiv ResearchGate Google Scholar
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
On reduced type in one dimensional analytic k-algebras (Morgantown Algebra Days, West Virginia University, April 2023)
The Frobenius Problem (Math Circle, Salt Lake City, University of Utah, April 2023)
Frobenius Problem and Numerical Semigroup Rings (Math For All, Salt Lake City, University of Utah, February 2023)
Module of Differentials and Berger's Conjecture (Algebra Seminar, University of Georgia, February 2023)
Discussions on Berger's Conjecture (Commutative Algebra Seminar, University of Utah, October 2022)
Notes on Berger's Conjecture (Graduate Students Seminar, University of Virginia, April 2022)
On Reflexive and I-Ulrich Modules (Joint Mathematics Meetings, April 2022)
Traceable PRFs: Full Collusion Resistance and Active Security (PKC, March 2022) (Video)
Torsion in the Module of Differentials (Special Session on Recent Developments in Commutative Algebra, Purdue University, March 2022)
Partial Trace Ideals and Berger's Conjecture (Virtual Commutative Algebra Seminar, University of Illinois at Chicago, January 2022)
Discussions on I-Ulrich Modules (Commutative Algebra Seminar, Purdue University, (Zoom meeting) April 2021)
An Introduction to Gröbner Bases (joint talk with Stephanie Shand) (Graduate Students Seminar, University of Virginia, April 2021) (Slides)
Discussions on I-Ulrich Modules ((Algebra Seminar, West Virginia University, Feb 2021) (Slides)
Discussions on Berger's Conjecture (Joint Mathematics Meeting January, 2021)
A Study of Colength in Dimension One (Commutative and Homological Algebra Market Presentations (CHAMP), October 14, 2020), (Research Elevator Pitch, Video)
Poster: An Approach To Berger's Conjecture (Early Commutative Algebra Researchers (eCARs), June 27-28, 2020); (Poster (Also Available Here)
A Simple Study of Colength (Summer 2020, New Mexico State University, Graduate Commutative Algebra Seminar)
An Approach to Berger's Conjecture (A Zoom Special Session
On Commutative Algebra, March 2020), (Video, Slides)
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.