My research area lies in the interface between algebraic geometry and combinatorics. More specifically, I am interested in the stability and positivity properties of toric vector bundles, moduli of (toric) vector bundles, and connections on principal bundles. I am also interested in tropical geometry and vector bundles on them. I have also worked on topological analogues of toric varieties, namely quasitoric manifolds and torus manifolds.
Toric vector bundles on Bott tower (with Jyoti Dasgupta), Bull. Sci. Math., Vol 155, 2019, 74-91, arXiv.
Cohomology of torus manifold bundles (with Jyoti Dasgupta and V. Uma ), Math. Slovaca, Vol 69, 2019, No. 3, 685-698, arXiv.
Equivariant K-theory of quasitoric manifolds (with Jyoti Dasgupta and V. Uma), Proc. Indian Acad. Sci. Math. Sci., Volume 129, Issue 5, November 2019, arXiv.
Stability of equivariant vector bundles over toric varieties (with Jyoti Dasgupta and Arijit Dey), Doc. Math., Volume 25, 1787-1833 (2020), arXiv.
Erratum to: ``Stability of equivariant vector bundles over toric varieties'' (with Jyoti Dasgupta and Arijit Dey), Doc. Math., Volume 26, 1271-1274 (2021).
Seshadri constants of equivariant vector bundles on toric varieties (with Jyoti Dasgupta and Aditya Subramaniam), J. Algebra, Volume 595, 38-68 (2022), arXiv.
Seshadri constants on Bott towers (with Indranil Biswas, Jyoti Dasgupta and Krishna Hanumanthu), J. Algebra, Volume 601, 178-197 (2022), arXiv.
Classification, reduction and stability of toric principal bundles (with Jyoti Dasgupta, Indranil Biswas, Arijit Dey and Mainak Poddar), Transform. Groups (2023), arXiv.
G-Connections on principal bundles over complete G-varieties (with Mainak Poddar), J. Pure Appl. Algebra (2024), arXiv.
Logarithmic connections on principal bundles over normal varieties (with Jyoti Dasgupta and Mainak Poddar), Bull. Sci. Math., Vol 206, 2026, arXiv.
Tropical Vector Bundles (with Diane Maclagan), preprint available at arXiv.
Seshadri constants and negative curves on blowups of ruled surfaces (with Cyril J. Jacob and Ronnie Sebastian), preprint available at arXiv.
Positivity of line bundles on general blow ups of Hirzebruch surfaces (with Cyril J. Jacob), preprint available at arXiv.
“Polytopes, cones and complexes” at the Algebra Seminar, IIT Madras, March 2016.
“Equivariant cohomology ring of smooth complete toric variety” at the Algebra Seminar, IIT Madras, November 2017.
“Positivity of line bundles on Bott tower” in Mathematics Department In-house Symposium, IIT Madras, October 7, 2018.
“Stability of equivariant vector bundles over toric varieties” in the Conference on Geometric Topology held at Bhaskaracharya Pratishthana Pune, December 6-8, 2019.
“Stability of tangent bundles over nonsingular toric varieties” in Postdoc Seminar, IISER Pune, March 13, 2020.
“Seshadri constants on Bott towers” in a symposium at the online conference Virtual Math Fest 2020 , July 20-26, 2020, Video Link.
“Seshadri constants on Bott towers” in Postdoc Seminar (online), IISER Pune, March 23, 2021.
“Seshadri constants of equivariant vector bundles on toric varieties'' in IISc-IISER Pune Twenty-20 Symposium (online), September 17-18, 2021, Video Link.
``On (semi)stability of equivariant vector bundle on toric varieties'' in Algebraic Geometry Seminar, The University of Warwick (online), February 16, 2022.
``Logarithmic connections on Principal bundles I'' in Joint Symposium (hybrid mode), Department of Mathematics, IISER Pune, 16-17 March 2022, Video Link (from 6:54:00).
``Seshadri constants of equivariant vector bundles on toric varieties'' in EDGE Geometry Seminar, Department of Mathematics, University of Edinburgh, 28 September 2022.
``Logarithmic connections on principal bundles over normal varieties'' in Indian Women and Mathematics (IWM) Annual Conference 2022-2023 , IISER Pune, 27-29 December 2022.
``Tropical Vector Bundles '' in Tropical geometry: Moduli spaces and matroids, Goethe University, Frankfurt am Main, 7 - 11 October 2024.
``Tropical Vector Bundles'' in Algebraic Geometry Seminar, IIT Bombay, 1 November 2024.
``Tropical Vector Bundles'' at the Algebraic Geometry Symposium in the 39th Annual Conference of the Ramanujan Mathematical Society at CHRIST (Deemed to be University), Bengaluru, December 27-29, 2024.
``Tropical Toric Vector Bundles'' at Mathematics Seminar, Chennai Mathematical Institute, April 10, 2025.
Lightning talk ``Tropical Toric Vector Bundles'' at the Summer School "Algebraic and tropical geometry of moduli spaces of curves ", University of Bologna, September 8-12, 2025.
Presented a poster titled “Positivity on Bott tower” in Conference on Commutative Algebra and Algebraic Geometry (CAAG) held at IISER Bhopal in July 2019.
Presented a poster titled ``Classification and reduction of toric principal bundles'' in VBAC 2022: Moduli Spaces and Vector Bundles - New Trends held at the University of Warwick, 25-29 July, 2022.
Presented a poster titled ``Classification and reduction of toric principal bundles'' in COMB in CAMB, Summer School on Combinatorial Methods in Algebraic Geometry held at the University of Cambridge, 5-9 September 2022.
Presented a poster titled ``Classification and reduction of toric principal bundles'' in V BrAG meeting held at Imperial College in London, 14-16 September 2022.
Presented a poster titled ``Seshadri constants of equivariant vector bundles on toric varieties'' in Vector Bundles in Chennai held at IIT Madras, Chennai, 6-11 February 2023.