# Ari Shnidman

Associate professor in mathematics at the Hebrew University of Jerusalem.

For the 2024/25 academic year I am a member of the Institute of Advanced Studies in Princeton.

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Address:

Institute of Advanced Studies

**Office**: Fuld 420

**Email**: ari.shnidman (at) gmail.com

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Research

My research interests are in number theory, especially arithmetic geometry, automorphic forms, and arithmetic statistics.
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Papers

Vanishing criteria for Ceresa cycles, with J. Laga, * preprint*.

Derivatives of Rankin-Selberg *L*-functions and heights of generalized Heegner cycles , with D. Lilienfeldt, *preprint*.

Ceresa cycles of bielliptic Picard curves, with J. Laga, * submitted*.

Rational torsion points on abelian surfaces with quaternionic multiplication, with J. Laga, C. Schembri, and J. Voight, to appear in *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, *submitted*.

Arbitrarily large *p*-torsion in Tate-Shafarevich groups, with E.V. Flynn and an appendix by T.A. Fisher, to appear in *J. Inst. Math. Jussieu*.

Integers expressible as the sum of two rational cubes, with L. Alpöge 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, to appear in *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, to appear in *Algebra & Number Theory*.

A positive proportion of quartic fields are not monogenic yet have no local obstruction to being so , with L. Alpöge 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. Alpöge and M. Bhargava, *submitted*.

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 *y*^{2} = x^{3} + 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*.

Néron-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).

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Conferences:

Number Theory and Arithmetic, Jeursalem 2024

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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).

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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

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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

HBWA 5, June 27, in Jerusalem.

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Funding: