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