Shiva Chidambaram

MIT Department of Mathematics
77 Massachusetts Ave. Bldg. 2-336
Cambridge, MA 02139

Email: shivac at mit dot edu
Office: 2-336
Pronouns: he/him

I am a Research Scientist at Massachusetts Institute of Technology as part of the Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation. My research interests are in algebraic number theory and arithmetic geometry focusing on Galois representations, with a keen interest in explicit methods.

I received my PhD from the University of Chicago under the guidance of Prof. Frank Calegari. I completed my Bachelors and Masters from IISER Pune. Here is my CV.

Research

Rational points on hyperelliptic Atkin-Lehner quotients of modular curves and their coverings, with N. Adžaga, T. Keller and O. Padurariu. Preprint. [arXiv]
Quadratic Chabauty for Atkin-Lehner Quotients of Modular Curves of Prime Level and Genus 4, 5, 6, with N. Adžaga, V. Arul, L. Beneish, M. Chen, T. Keller and B. Wen. Preprint. [pdf] [arXiv]
Mod \(p\) Galois representations not arising from abelian varieties. Preprint. [pdf] [arXiv]
Here is an exposition of the work by Frank Calegari.
Rationality of twists of the Siegel modular variety of genus 2 and level 3, with F. Calegari. Proceedings of the American Mathematical Society (150) 2022, p 1975-1984. [pdf] [arXiv] [Journal]
Magma code and output.
Here is an exposition of the work by Frank Calegari.
Abelian surfaces with fixed 3-torsion, with F. Calegari and D. Roberts. pp. 91--108, Proceedings of the Fourteenth Algorithmic Number Theory Symposium (ANTS-XIV), edited by Steven Galbraith, Open Book Series 4, Mathematical Sciences Publishers, Berkeley, 2020. [pdf] [arXiv] [Journal]
Mathematica codes.
Here are the slides of my talk at ANTS-XIV. Here is an expository account of our work by Frank Calegari.
Some modular abelian surfaces, with F. Calegari and A. Ghitza. Mathematics of Computation (89) 2020, no. 321, p 387-394. [pdf] [arXiv] [Journal]

Teaching

2020-2021 MATH 19620 - Linear Algebra, Winter 2021.
2019-2020 MATH 152 - Calculus II, Autumn 2019; MATH 153 - Calculus III, Winter 2020.
2018-2019 MATH 151 - Calculus I, Autumn 2018; MATH 152 - Calculus II, Winter 2019; MATH 153 - Calculus III, Spring 2019.
2017-2018 MATH 152 - Calculus II, Autumn 2017; MATH 153 - Calculus III, Winter 2018; MATH 19620 - Linear Algebra, Spring 2018.
2016-2017 College Fellow for the MATH 161-162-163 sequence - Honors Calculus (IBL).