Shubham Sinha

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 algebraic geometry; Algebraic combinatorics. In particular, I am interested in curve counting and enumerative invariants.

Email: ssinha1 at ictp.it
Office: LB-108, ICTP

Preprint

• Quantum K-Invariants via Quot schemes I (with Ming Zhang)
• Quantum K-Invariants via Quot schemes II (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)

Teaching

• Complex Analysis: Fall 2024, ICTP
• Calculus 1 (Math 10A): Summer 2023, UC San Diego
• Calculus 2 (Math 10B): Summer 2022, UC San Diego
• Calculus 2 (Math 10B): Summer 2021, UC San Diego

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.

Research Talk

• GAAG seminar, EPFL Lausanne (2024) : K-theoretic invariants of the Quot scheme of curves.
• Algebra and Number Theory Seminar, University of Vienna (2024) : K-theoretic invariants of the Quot scheme of curves.
• Moduli stacks and enumerative geometry (VBAC), Isaac Newton Institute, Cambridge (2024) : Quantum K-invariants via Quot schemes. video, 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.

Seminars

• ICTP/SISSA Research Seminar on Quot schemes – Fall 2024
• TRINO: A 3-fold seminar in Trieste (ICTP - SISSA - UniTS)