Ari Shnidman

ari shnidman Welcome!
I'm an associate professor in mathematics at Temple University in Philadelphia.
Warning: some links below may not work while this site is under construction.
Email: ari.shnidman (at) gmail.com

Address:
608 Wachman Hall
Department of Mathematics
1805 North Broad Street
Philadelphia, PA 19122

Research

My research interests are in number theory, especially arithmetic geometry, special values of L-functions, and arithmetic statistics.

Teaching

In Spring 2026, I'm teaching MATH 8012: Abstract Algebra II (Graduate)

Papers

  • Hecke reciprocity and class groups, with A. Siad, preprint.
  • Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field, with L. Alpoge, M. Bhargava, and W. Ho, to appear in Inventiones mathematicae.
  • Vanishing criteria for Ceresa cycles, with J. Laga, to appear in Compositio Mathematica.
  • Derivatives of Rankin-Selberg L-functions and heights of generalized Heegner cycles , with D. Lilienfeldt, submitted.
  • Ceresa cycles of bielliptic Picard curves, with J. Laga, J. Reine Angew. Math.
  • Rational torsion points on abelian surfaces with quaternionic multiplication, with J. Laga, C. Schembri, and J. Voight, Forum of Mathematics, Sigma.
  • The geometry and arithmetic of bielliptic Picard curves, with J. Laga, submitted.
  • Normal distribution of bad reduction, with R. Lemke Oliver and D. Loughran, Ramanujan Journal.
  • Arbitrarily large p-torsion in Tate-Shafarevich groups, with E.V. Flynn and an appendix by T.A. Fisher, J. Inst. Math. Jussieu.
  • Integers expressible as the sum of two rational cubes, with L. Alpoge and M. Bhargava and an appendix by A. Burungale and C. Skinner, submitted. (popular article)
  • Experiments with Ceresa classes of cyclic Fermat quotients, with D. Lilienfeldt, Proceedings of the AMS.
  • Rank growth of elliptic curves over N-th root extensions, with A. Weiss, Transactions of the AMS.
  • Sandpile groups of supersingular isogeny graphs, with N. Munier, Journal de Theorie des Nombres de Bordeaux.
  • Elements of prime order in Tate-Shafarevich groups of abelian varieties over ℚ , with A. Weiss, Forum of Mathematics, Sigma.
  • Ranks of abelian varieties in cyclotomic twist families, with A. Weiss, Algebra & Number Theory.
  • A positive proportion of quartic fields are not monogenic yet have no local obstruction to being so , with L. Alpoge and M. Bhargava, Mathematische Annalen.
  • Manin-Drinfeld cycles and derivatives of L-functions, JEMS.
  • Genus two curves with full √ 3 level structure, with N. Bruin and E.V. Flynn, Selecta Mathematica. (sage code)
  • A positive proportion of cubic fields are not monogenic yet have no local obstruction to being so, with L. Alpoge and M. Bhargava, Mathematische Annalen.
  • Elements of given order in Tate-Shafarevich groups of abelian varieties in quadratic twist families, with M. Bhargava, Z. Klagsbrun, and R. Lemke Oliver, Algebra & Number Theory.
  • Quadratic twists of abelian varieties with real multiplication, IMRN.
  • A Gross-Kohnen-Zagier formula for Heegner-Drinfeld cycles, with B. Howard, Advances in Mathematics.
  • The average size of the 3-isogeny Selmer groups of elliptic curves y2 = x3 + k, with M. Bhargava and N. Elkies, Journal of the LMS.
  • Grothendieck groups of categories of abelian varieties, European Journal of Mathematics.
  • Three-isogeny selmer groups and ranks of abelian varieties in quadratic twist families over a number field, with M. Bhargava, Z. Klagsbrun, and R. Lemke Oliver, Duke Math Journal.
  • Extensions of CM elliptic curves and orbit counting on the projective line, with J. Rosen, Research in Number Theory.
  • p-adic heights of generalized Heegner cycles, Annales de l'Institute Fourier.
  • Neron-Severi groups of product abelian surfaces, with J. Rosen.
  • Heights of generalized Heegner cycles, Ph.D. thesis, University of Michigan.
  • On the number of cubic orders of bounded discriminant having automorphism group C3, and related problems, with M. Bhargava, Algebra & Number Theory.
  • Grand orbits of integer polynomials, with M. Zieve (appendix with B. Seward).

    Conferences co-organized:

  • Number Theory and Arithmetic, Jerusalem 2024
  • Algebraic Points on Curves, ICERM, Providence, June 2025

    Slides:

  • Sums of two rational cubes: ICTS workshop (Aug 2022).
  • Vanishing of Ceresa cycles: vANtAGe seminar (Aug 2024).
  • Ceresa cycles: Explicit methods in number theory (Sep 2024).

    Seminars:

  • Lunch seminar on Transcendental Number Theory (Spring 2024)
  • Lunch seminar on explicit methods in number theory (Fall 2023)
  • Honda-Tate and applications seminar (Spring 2023)
  • Fundamental Lemmas and Fourier Transform (Spring 2021)
  • Number Theory and Algebraic Geometry Lunch Seminar

    HUJI-BGU Workshop in Arithmetic

  • HUJI-BGU 1 -- Tate modules of elliptic curves and abelian varieties
  • HUJI-BGU 2 -- L-functions for GL(1) and regulators
  • HUJI-BGU 3 -- Arithmetic geometery of locally symmetric spaces
  • HUJI-BGU 4 -- Research talks
  • HUJI-BGU 5, June 27, in Jerusalem.