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. I am interested in enumerative problems arising in algebraic geometry.

Papers

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

• 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)

Teaching:

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

Research Presentations

• 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.

Outreach

• Olympiad : I was involved in training Indian IMO (International Mathematical Olympiad) team during the years 2014-2017 and 2021.
• Mentoring at UCSD : I mentored a group of undergraduate students at UCSD, in Spring 2020, as part of UCSD's RTG grant. We discussed basics of algebraic geometry and classical theorem : '27 lines on a cubic surface'.

Teaching Assistance:

I was a teaching assistant for the following courses at UC San Diego:

1. Spring 2022 - Math 120B Applied Complex Analysis
2. Winter 2022 - Math 120A Applied Complex Analysis
3. Fall 2021 - Math 109 Mathematical reasoning
4. Spring 2021 - Math 220C Complex Analysis ; Math 154 Discrete Math & Graph Theory
5. Winter 2021 - Math 220B Complex Analysis ; Math 103A Modern Algebra
6. Fall 2020 - Math 220A Complex Analysis
7. Spring 2020 - Math 20E Vector Calculus
8. Winter 2020 - Math 103B Modern Algebra
9. Fall 2019 - Math 103A Modern Algebra
10. Spring 2019 - 20E Vector Calculus
11. Winter 2019 - 104B Number Theory and 20A Calculus
12. Fall 2018 - 104A Number Theory
13. Spring 2018 - 184 Enumerative Combinatorics
14. Winter 2018 - 154 Discrete Math & Graph Theory
15. Fall 2017 - 10A Calculus