Research

My area of research is Commutative Algebra. I am particularly interested in algebraic theory of D-modules, local cohomology and methods of prime characteristic.

Research Projects:

Mathematical Research Impact Centric Support (MATRICS) grant for the research project "Classification of Forbenius Forms and F-pure threshold" by Science and Engineering Research Board (SERB), India. (2022-2025)
Early Career Research Award for the research project “Study of Local Cohomology by using the theory of D-modules” by Science and Engineering Research Board (SERB), India. (2018-2021).

Publications:

F-threshold of determinantal rings with Barbara Betti, Alessio Moscariello, and Francesco Romeo. arXiv: 2309.17376 [math.AC].
On the graded injective hull of R/p in prime characteristic (with Aarti Patle) to appear in Journal of Algebra and its Applications.
On invariants of modules over the ring of differential operators (with Aarti Patle), Bulletin of the Malaysian Mathematical Sciences Society Vol 45, pp. 2619–2637, 2022.
Lower Bounds on the F-pure Threshold and Extremal Singularities (with Zhibek Kadyrsizova, Jennifer Kenkel, Janet Page, Karen E. Smith, Adela Vraciu, and Emily E. Witt), Transactions of the American Mathematical Society. Ser. B, Volume 9, Pages 977–1005, 2022.
Classifications of Frobenius forms in dimension five (with Zhibek Kadyrsizova, Janet Page, Karen E. Smith, Adela Vraciu, and Emily E. Witt ), Women in Commutative Algebra. Association for Women in Mathematics Series, Vol 29, 2021.
Cubic Surfaces of Characteristic Two (with Zhibek Kadyrsizova, Jennifer Kenkel, Janet Page, Karen E. Smith, Adela Vraciu, and Emily E. Witt), Transactions of the American Mathematical Society Vol. 374, No. 09, pp. 6251–6267, 2021.
Generalized Eulerian D-modules in Char p > 0 (with Aarti Patle), Journal of Algebra and its Applications, Vol. 20, No. 07, 2150127, 2021.
On Derived Functors of Graded Local Cohomology Modules II (with Tony J. Puthenpurakal and Sudeshna Roy), Illinois Journal of Mathematics, Vol 64 (4), pp. 595-612, 2020.
On Derived Functors of Graded Local Cohomology Modules (with Tony J. Puthenpurakal), Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 167 (3), pp. 549-565, 2019.
Mathematical Counterpart of the Heisenberg Uncertainty Principle (with Shiv Datt Kumar), Reports on Mathematical Physics, 80, pp. 161-176, 2017.
Rees Algebra over an Ideal in t-Rings (with Shiv Datt Kumar), Journal of Pure and Applied Algebra, 219 , pp. 830-838, 2015.
On the Involutivity of the Characteristic Variety (with Shiv Datt Kumar), Communications in Algebra, 42, pp. 3607-3618, 2014.