Shubhankar Sahai

Email: ssahai (at) ucsd (dot) edu
Office: HSS 3073

I am a 4th year graduate student in the math department at UCSD.
I work in arithmetic and algebraic geometry. Some of my work is motivated by algebraic K-theory.
My advisor is Kiran Kedlaya.

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Research

I am broadly interested in algebraic and arithmetic geometry. See below for things I have thought about in the past.

Preprints

• Duality of differential operators and algebraic de Rham cohomology — with Caleb Ji, Casimir Kothari, Oliver Li, Sveta Makarova and Sridhar Venkatesh. (We hope to generalise the ideas in this paper in a second version.)
• A note on the syntomification of closed immersions. (In preparation).

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Teaching

UCSD

I have been a TA for the following courses

• Math 187A—Introduction to Cryptography: Winter 2023, Spring 2023, Winter 2024, Spring 2024, Fall 2024
• Math 20D—Introduction to Differential Equations: Fall 2022
• Math 20E—Vector Calculus: Fall 2021, Winter 2022, Spring 2022

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Seminars

There is a discord server for UCSD students (graduate or undergraduate) and post-docs interested in arithmetic geometry and related topics. Most (but not all!) student seminars in these topics are organised through that server. Please email me if you are UCSD affiliated and want to join!

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Miscellaneous

Undergrad research

• Composition Tableaux basis for Schur functors and the Plücker algebra: Gives a representation theoretic interpretation of certain combinatorial objects called Row-Strict Composition Tableaux (RSCT) and variants. This has been pending revision, in accordance with referee review, for some time, and hopefully can be revised in finite time.