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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: During my PhD, I also was engaged in reading and reasearching various topics in Cryptography with Prof. David Wu.

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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

  • 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.