I am a postdoctoral fellow at the International Centre for Theoretical Physics in Trieste, Italy. My mentor is Prof. Alina Marian. I received my Ph.D. from the department of mathematics at the University of California San Diego in June 2023. My advisor was Prof. Dragos Oprea.
Here is my CV.
Research Area: Enumerative Geometry; Algebraic Combinatorics. In particular, I am interested in curve counting and enumerative invariants.
Preprint
- Quantum K-Invariants via Quot schemes I (with Ming Zhang)
Papers
- Euler characteristics of tautological bundles over Quot schemes of curves. Advances in Mathematics 418 (2023) (with Dragos Oprea)
- The virtual intersection theory of isotropic Quot Schemes. Journal of Geometry and Physics 198 (2024)
- Cores of partitions in rectangles. Electronic Journal of Combinatorics 31(1) (2024) (with Arvind Ayyer)
- Bergman-Einstein metrics on two-dimensional Stein spaces. To appear in Michigan Mathematical Journal (with Soumya Ganguly)
- The size of t-cores and hook lengths of random cells in random partitions. The Annals of Applied Probability 33 (2022) (with Arvind Ayyer)
- Random t-Cores and Hook Lengths in Random Partitions. Sém. Lothar. Combin. 84B (2020) (with Arvind Ayyer)
- Driving chemical reactions with polariton condensates. Nature Communications 1645 (2022) (with Sindhana Pannir-Sivajothi, Jorge A. Campos-Gonzalez-Angulo, Luis A. Martínez-Martínez, Joel Yuen-Zhou)
- Numerical invariants of Quot schemes of curves . Ph.D. Thesis (2023)
Research Presentations
- Moduli stacks and enumerative geometry (VBAC), Isaac Newton Institute, Cambridge (2024) : Quantum K-invariants via Quot schemes. slides
- Virginia Tech Algebra Seminar (2024) : Quantum K-invariants via Quot scheme.
- Algebraic Geometry Seminar, IISER Pune (2024) : Quantum K-invariants of Grassmannians via Quot scheme.
- Algebraic Geometry Seminar, ICTP (2023) : Quantum K-invariants of Grassmannians via Quot scheme.
- Categorical methods in moduli theory, University of Pennsylvania (2023) : Schur bundles over Quot schemes of P^1 (slides).
- Algebraic Geometry Seminar, ICTP (2023) : Tautological bundles over Quot schemes on curves (slides).
- Geometry & Topology Seminar, IISc Bangalore (2023) : The virtual intersection theory of isotropic Quot schemes.
- Virginia Tech Algebra Seminar (2022) : Numerical invariants of Quot schemes on curves.
- Western Algebraic Geometry Symposium (WAGS), UC Riverside (2022) : Tautological bundles over Quot schemes of curves (poster).
- University of Warwick, VBAC (2022) : Tautological bundles over Quot schemes of curves (poster).
- Richmond Geometry festival (2022) : Tautological bundles over Quot schemes of curves (poster).
- FPSAC 2020 : Random t-cores and hook lengths in random partitions (video, slides).
- IMSc Algebraic Combinatorics Seminar (2020) : Random t-cores and hook lengths in random partitions.
Mentoring Activity
- Olympiad: I was involved in training the Indian IMO (International Mathematical Olympiad) team during the years 2014-2017 and 2021.
- Mentoring at UCSD: RTG graduate directed reading for undergraduates, Algebraic curves and Riemann surfaces, Spring 2021.
- Mentoring at UCSD: RTG graduate directed reading for undergraduates, 27 lines on a cubic surface, Spring 2020.