Supravat Sarkar

About

Hi! I'm a fifth year PhD student in the Mathematics department at Princeton University, where I'm fortunate to be advised by János Kollár and Jakub Witaszek. This year I am in the job market looking for Postdoctorate positions.

Research Interests

I am interested in several topics in algebraic geometry. Some of my particular interests are: birational geometry, study of contractions of special kind of varieties, classical algebraic geometry, vector bundles and projective bundles, automorphisms and endomorphisms of varieties, singularity theory, punctual Hilbert scheme, Quot scheme, topology of varieties. I am also very interested in complex geometry and topology.

Preprints and Publications

1. Proof of Miyanishi's conjecture on endomorphisms of varieties
   Supravat Sarkar
   Preprint
2. Automorphisms of punctual Hilbert schemes and symmetric powers of varieties
   Ashima Bansal, Supravat Sarkar, Shivam Vats
   Preprint — Aug 2025
3. Frobenius liftable hypersurfaces
   Tatsuro Kawakami, Supravat Sarkar, Jakub Witaszek
   Preprint — Jul 2025
4. Torelli theorems for Quot schemes of vector bundles on curves
   Ashima Bansal, Supravat Sarkar, Shivam Vats
   Preprint
5. Tangent bundles of Quot schemes of vector bundles on curves
   Ashima Bansal, Supravat Sarkar, Shivam Vats
   Preprint
6. Tangent bundle of punctual Hilbert scheme and distinguishing products of varieties
   Supravat Sarkar
   Preprint
7. Stable and unstable syzygy bundles on certain Picard rank one varieties
   Supravat Sarkar
   Preprint
8. Extension of Ulrich bundles
   Supravat Sarkar
   Preprint
9. Singularity of Q-divisors of multidegree one in multiprojective space
   Supravat Sarkar
   Accepted for publication in the journal “Michigan Mathematical Journal”
10. Singularity of cubic hypersurfaces and hyperplane sections of projectivized tangent bundle of projective space
    Ashima Bansal, Supravat Sarkar, Shivam Vats
    Published in "Proceedings of the American Mathematical Society"
11. Generalized determinantal representation of hypersurfaces
    A. El Mazouni, D. S. Nagaraj, Supravat Sarkar
    Accepted for publication in the journal "Bulletin des sciences mathématiques"
12. Descend of morphisms of varieties
    Supravat Sarkar
    Accepted for publication in the journal "Mathematical Research Letters"
13. Automorphisms of very general blow up
    Supravat Sarkar
    Preprint
14. Isomorphisms and automorphisms of multiprojective bundles and symmetric powers of projective bundles
    Ashima Bansal, Supravat Sarkar, Shivam Vats
    Accepted for publication in the journal "Bulletin des sciences mathématiques"
15. Symmetric power of higher dimensional varieties
    Ashima Bansal, Supravat Sarkar, Shivam Vats
    Accepted to be published in Journal of Pure and Applied Algebra
16. Images of toric variety and amplified endomorphism of weak Fano threefolds
    Supravat Sarkar
    Preprint — Jun 2025
17. Smooth blow up structures on projective bundles
    Supravat Sarkar
    Accepted to be published in Annali della Scuola Normale Superiore di Pisa
18. Varieties with two smooth blow up structures
    Supravat Sarkar
    Preprint — Sep 2024
19. Extremal Contraction of Projective Bundles
    Ashima Bansal, Supravat Sarkar, Shivam Vats
    Preprint — Sep 2024
20. Isomorphism of Multiprojective Bundles and Projective Towers
    Ashima Bansal, Supravat Sarkar, Shivam Vats
    Accepted to be published in Kyoto Journal of Mathematics
21. Characters of modules over negative rank-2 Borcherds--Kac--Moody Lie algebras
    Souvik Pal, Supravat Sarkar and G. Krishna Teja
    Preprint
22. Average order in regular wreath products
    Supravat Sarkar
    Published in “International Journal of Group Theory”
23. A Combinatorial Proof of a generalization of a Theorem of Frobenius
    Supravat Sarkar
    Published in the journal “The Mathematics Student”, Indian Mathematical Society
24. The Weingarten map and curvatures of SL(n, R)
    Supravat Sarkar
    Published in the journal “Mathematics Newsletter”, Ramanujan Mathematical Society, September 2020
25. New proofs to Erdös-Hajnal and Gallai upper bounds of chromatic number
    Supravat Sarkar
    Published in the journal “Mathematics Newsletter”, Ramanujan Mathematical Society, September-December 2024

Teaching

I have been a Teaching Assistant for the following courses at Princeton:

MAT 457: Algebraic Geometry (Fall 2026)

MAT 447: Commutative Algebra (Spring 2026)

MAT 345: Algebra I (Fall 2025)

MAT 202: Linear Algebra with Applications (Spring 2025)

MAT 345: Algebra I (Fall 2024)

MAT 330: Complex Analysis with Applications (Spring 2024)

Hartshorne's Algebraic Geometry Chapter 1, Spring 2026

Algebraic Curves (Algebraic Curves, William Fulton), Fall 2025

Riemann Surfaces (Algebraic Curves and Riemann Surfaces, Rick Miranda), Spring 2025

Contact Information