Home Research Teaching Purdue CA Seminar

Research Interests

My research is in Commutative Algebra. Some keywords are: positive characteristic techniques, invariant theory, determinantal varieties, differential operators, linkage and residual intersections, local cohomology modules, Stanley--Reisner theory.

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Preprints and Publications

  1. The arithmetic rank of determinantal nullcones
    with Jack Jeffries, Anurag K. Singh, and Uli Walther
    Preprint, 52 pp.
  2. 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.
  3. Symbolic powers of the generic linkage of maximal minors
    with Matteo Varbaro
    Preprint, 25 pp.
  4. F-purity and the F-pure threshold as invariants of linkage
    Preprint, 23 pp.
  5. On the natural nullcones of the symplectic and general linear groups
    with Yevgeniya Tarasova and Uli Walther
    Journal of the London Mathematical Society, Volume 11 (2025), e70078, 31 pp.
  6. Linkage and F-regularity of determinantal rings
    with Yevgeniya Tarasova
    International Mathematics Research Notices, Volume 11 (2024), pp. 9323–9339.
  7. When are the natural embeddings of classical invariant rings pure?
    with Mel Hochster, Jack Jeffries, and Anurag K. Singh
    Forum of Mathematics, Sigma, Volume 11 (2023), Paper no. e67, 43 pp.
  8. Counting geometric branches via the Frobenius map and F-nilpotent singularities
    with Hailong Dao and Kyle Maddox
    Nagoya Mathematical Journal, Volume 255 (2024), pp. 724–741.
  9. Homological properties of pinched Veronese rings
    with Kyle Maddox
    Journal of Algebra, Volume 614 (2023), pp. 307–329.
  10. Cohomological dimension of ideals defining Veronese rings
    Proceedings of the American Mathematical Society, Volume 149, no. 4 (2021), pp. 1387–1393.

Undergraduate Research

  1. A Dedekind domain with nontrivial class group
    with Sagar Shrivastava and B. Sury
    The American Mathematical Monthly, Volume 125, Issue 4 (2018), pp. 356–359.
  2. On the prime ideals of C[0,1]
    Resonance (Indian Academy of Sciences), May 2016, pp. 439–446.

Upcoming Research Travel