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Research Interests

My research interests lie in Commutative Algebra. I work with Noetherian commutative local rings and most of my research questions arose primarily while working on a longstanding open problem concerning the torsion of the module of Kähler differentials. I made new progress on this and the question is still wide open. Simultaneously, I have contributed towards many other problems using a variety of techniques, for instance:

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

  • Annihilators of (co)homology and their influence on the trace Ideal, with Justin Lyle (Submitted) arXiv version

  • Two Criteria for Quasihomogeneity, with Vivek Mukundan; Proceedings of the American Mathematical Society 152.06 (2024): 2369-2375

  • 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; Journal of Algebra 652: 1-19, 2024 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 Nearly Gorenstein Rings and a Generalization of a Conjecture of Tachikawa (Special Session on Singularities in Commutative Algebra, University at Albany, October 2024)

  • On Nearly Gorenstein Rings and a Generalization of a Conjecture of Tachikawa (Special Session on Topics in Commutative Algebra and Algebraic Geometry, Georgia Southern University, October 2024)

  • Reduced type of one dimensional complete local domains (AMS Special Session on Commutative algebra and connections to combinatorics, University of Texas – San Antonio, September 2024)

  • On reduced type in one dimensional analytic k-algebras (Joint Mathematics Meetings January 2024)

  • 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.