Home Research Teaching Purdue CA Seminar

Research Interests

My research is in Commutative Algebra and its interactions with Algebraic Geometry and Combinatorics. Some keywords are: positive characteristic techniques, invariant theory, determinantal varieties, differential operators, linkage and residual intersections, local cohomology modules, symbolic powers.

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Preprints and Publications

  1. The arithmetic rank of the residual intersections of a complete intersection ideal
    with Manav Batavia, Kesavan Mohana Sundaram, and Taylor Murray
    Preprint, 20 pp. [arXiv]
  2. The arithmetic rank of determinantal nullcones
    with Jack Jeffries, Anurag K. Singh, and Uli Walther
    Preprint, 52 pp. [arXiv]
  3. Bounds on the plus-pure thresholds of some hypersurfaces in (ramified) regular rings
    with Marta Benozzo, Vignesh Jagathese, Pedro Ramírez-Moreno, Karl Schwede, and Prashanth Sridhar
    Preprint, 22 pp. [arXiv]
  4. Symbolic powers of the generic linkage of maximal minors
    with Matteo Varbaro
    Preprint, 25 pp. [arXiv]
  5. F-purity and the F-pure threshold as invariants of linkage
    Preprint, 23 pp. [arXiv]
  6. On the natural nullcones of the symplectic and general linear groups
    with Yevgeniya Tarasova and Uli Walther
    Journal of the London Mathematical Society, (2025). [arXiv] [Journal]
  7. Linkage and F-regularity of determinantal rings
    with Yevgeniya Tarasova
    International Mathematics Research Notices, (2024). [arXiv] [Journal]
  8. When are the natural embeddings of classical invariant rings pure?
    with Mel Hochster, Jack Jeffries, and Anurag K. Singh
    Forum of Mathematics, Sigma, (2023). [arXiv] [Journal]
  9. Counting geometric branches via the Frobenius map and F-nilpotent singularities
    with Hailong Dao and Kyle Maddox
    Nagoya Mathematical Journal, (2024). [arXiv] [Journal]
  10. Homological properties of pinched Veronese rings
    with Kyle Maddox
    Journal of Algebra, (2023). [arXiv] [Journal]
  11. Cohomological dimension of ideals defining Veronese rings
    Proceedings of the American Mathematical Society, (2021). [arXiv] [Journal]

Undergraduate Research

  1. A Dedekind domain with nontrivial class group
    with Sagar Shrivastava and B. Sury
    The American Mathematical Monthly, (2018).
  2. On the prime ideals of C[0,1]
    Resonance (Indian Academy of Sciences), (2016).

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