Shiva Chidambaram

Publications and Preprints

  1. On reducible \(\ell\)-torsion representations of Picard curves,
    with Xiyao Chen, Andrew Coursin, Erik Reed and Leo Yang.
    [pdf] [arXiv]
    Github repo containing Magma implementation of algorithms and data.
    Growing out of projects mentored through the Madison Experimental Mathematics (MXM) Lab

  2. Computing residual representations of abelian threefolds with imaginary multiplication,
    with P. Goodman.
    [pdf] [arXiv]
    Github repo containing Magma implementation of algorithms and data.
    Notes from my talk at Harvard NT seminar in 2024, and slides of my talk at JMM 2023 (a bit outdated).

  3. Point counts of abelian varieties over finite fields determining their zeta function,
    with Timo Keller.
    Submitted.
    [pdf] [arXiv]
    Github repo containing relevant Sage scripts and Lean formalization code.

  4. On the Visibility category of the Shafarevich--Tate group,
    with Barinder Banwait and Jerson Caro.
    Submitted.
    [pdf] [arXiv]
    Github repo containing relevant Magma codes.

  5. Computing the mod-3 Galois image of a principally polarized abelian surface over the rationals.
    LuCaNT: Databases, Algorithms, and Computational Number Theory, Contemporary Mathematics.
    [pdf] [arXiv] [Journal]
    Github repo containing relevant Magma codes.
    Video and Slides from talk at LuCaNT 2025.

  6. 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.

  7. Fekete polynomials of principal Dirichlet characters,
    with Ján Mináč, Tung T. Nguyen and Nguyen Duy Tân.
    Journal of Experimental Mathematics, 1(1), 51-93.
    [pdf] [arXiv] [Journal]

  8. 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 containing Sage implementation of algorithms and data.

  9. 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.

  10. 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.

  11. 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.

  12. 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]
    Repository with Mathematica codes and data.
    Here are the slides of my talk at ANTS-XIV. Here is an exposition of our work by Frank Calegari.

  13. Some modular abelian surfaces,
    with F. Calegari and A. Ghitza.
    Mathematics of Computation (89) 2020, no. 321, p 387-394.
    [pdf] [arXiv] [Journal]

In preparation

  1. Explicit families of abelian threefolds with imaginary multiplication and attached elliptic curves,
    with Pip Goodman.
    Slides from my talk at BU NT seminar available by request.
  2. Bad primes for invariants of CM Picard curves,
    with Yingkun Li and Brandon Williams.

Other writings