Shiva Chidambaram

Portrait picture 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.

My PIs at MIT are Bjorn Poonen and Drew Sutherland. 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

Publications

  1. Mod \(p\) Galois representations not arising from abelian varieties.
    J. Number Theory 259C (2024) pp. 219-237 [pdf] [arXiv] [Journal]
    Here is an exposition of the work by Frank Calegari.
  2. Fekete polynomials of principal Dirichlet characters, with Ján Mináč, Tung T. Nguyen and Nguyen Duy Tân.
    To appear in J. Exp. Math. [arXiv]
  3. Computing isogeny classes of typical principally polarized abelian surfaces over the rationals, with R. van Bommel, E. Costa and J. Kieffer.
    LuCaNT: LMFDB, computation, and number theory, 187-214. Contemporary Mathematics, 796. [pdf] [arXiv] [Journal]
    Github repo.
  4. Rational points on hyperelliptic Atkin-Lehner quotients of modular curves and their coverings, with N. Adžaga, T. Keller and O. Padurariu.
    Fifteenth Algorithmic Number Theory Symposium (ANTS XV), Research in Number Theory 8 (2022) no.4, Paper No. 87, 24 pp. [pdf] [arXiv] [Journal]
    Github repo containing relevant Magma codes.
  5. 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.
    Acta Arithmetica 208 (2023), p 15-49. [pdf] [arXiv] [Journal]
    Github repo containing relevant Magma codes.
  6. 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 our work by Frank Calegari.
  7. 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 exposition of our work by Frank Calegari.
  8. Some modular abelian surfaces, with F. Calegari and A. Ghitza.
    Mathematics of Computation (89) 2020, no. 321, p 387-394. [pdf] [arXiv] [Journal]

Preprints

  1. Galois images of Picard curves, with P. Goodman.
    Here are the slides of my talk at JMM 2023 (a bit outdated), and slides from PANTS 2023.

Teaching

Massachusetts Institute of Technology

University of Chicago

IISER Pune

Useful links

Other things of interest

Life

Books