Shubham Sinha

I am a Ph.D. student at the department of mathematics, UC San Diego, working with Prof. Dragos Oprea. I graduated from IISc, Indian Institue of Science, with a bachelor's degree in 2017.

Research Area: Algebraic Geometry; combinatorics. In particular, I am interested in curve counting and enumerative invariants.

Papers

• Euler characteristics of tautological bundles over Quot schemes of curves. (accepted) Advances in Mathematics [arXiv] (2022)
  (with Dragos Oprea)

• The virtual intersection theory of isotropic Quot Schemes.[arXiv] (2021)
  

• Bergman-Einstein metrics on two-dimensional Stein spaces[arXiv] (2022)
  (with Soumya Ganguly)

• The size of t-cores and hook lengths of random cells in random partitions. (accepted) Annals of Applied Probability [arXiv] (2019)
  (with Arvind Ayyer)
• Random t-Cores and Hook Lengths in Random Partitions Sém. Lothar. Combin. 84B (2020) [pdf]
  (with Arvind Ayyer)
  
• Driving chemical reactions with polariton condensates. Nature Communications. 1645 (2022)[arXiv]
  (with Sindhana Pannir-Sivajothi, Jorge A. Campos-Gonzalez-Angulo, Luis A. Martínez-Martínez, Joel Yuen-Zhou)

Research Presentations

• Algebraic Geometry Seminar, ICTP (2023) : Tautological bundles over Quot schemes on curves.
• Geometry & Topology Seminar, IISc Bangalore (2023) [Link] : The virtual intersection theory of isotropic Quot schemes.
• Virginia Tech Algebra Seminar (2022) [Link] : Numerical invariants of Quot schemes on curves.
• Western Algebraic Geometry Symposium (WAGS), UC Riverside (2022)[Link] : Tautological bundles over Quot schemes of curves. (poster)
• University of Warwick, VBAC (2022)[Link] : Tautological bundles over Quot schemes of curves. (poster)
• Richmond Geometry festival (2022)[Link] : Tautological bundles over Quot schemes of curves. (poster)
• FPSAC 2020 : July 15,2020;[FPSAC] : Random t-cores and hook lengths in random partitions.
  [Video] [Slides]
• IMSc Algebraic Combinatorics Seminar : June 18, 2020;[Link] : Random t-cores and hook lengths in random partitions.

Old News Seminar Fall 2022

Outreach

• Olympiad : I was involved in training Indian IMO (International Mathematical Olympiad) team during the years 2014-2017 and 2021.
• Mentoring at UCSD : RTG graduate directed reading for undegraduates, Algebraic curves and Riemann surfaces, Spring 2021.
• Mentoring as UCSD : RTG graduate directed reading for undegraduates, 27 lines on a cubic surface, Spring 2020

Teaching:

You can find the complete list of the courses I have taught here: Link

• Math 10B : Summer Session 1, 2022 at UCSD
• Math 10B : Summer Session 2, 2021 at UCSD