# Ari Shnidman

I am a postdoc in the Boston College math department.

I received my Ph.D. from the University of Michigan in May 2015. My advisor there was Kartik Prasanna.

I am currently applying for tenure-track positions (Fall 2017).

**Office**: Maloney 553

**Email**: shnidman (at) bc (dot) edu

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Research

My research interests are in arithmetic geometry and arithmetic statistics.
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Papers

Quadratic twists of abelian varieties with real multiplication, *submitted*.

Tate-Shafarevich groups of elliptic curves in quadratic twist families, with M. Bhargava, Z. Klagsbrun, and R. Lemke Oliver, *preprint*.

A Gross-Kohnen-Zagier formula for Heegner-Drinfeld cycles, with B. Howard, *submitted*.

The average size of the 3-isogeny Selmer groups of elliptic curves y^{2} = x^{3} + k, with M. Bhargava and N. Elkies, *submitted*.

Grothendieck groups of categories of abelian varieties, to appear in *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, *submitted*.

Extensions of CM elliptic curves and orbit counting on the projective line, with J. Rosen, to appear in *Research in Number Theory*.

*p*-adic heights of generalized Heegner cycles, *Annales de l'Institute Fourier* 66 no. 3 (2016), p. 1117-1174.

Néron-Severi groups of product abelian surfaces, with J. Rosen, *submitted* (2016).

Heights of generalized Heegner cycles, Ph.D. thesis, University of Michigan, (2015).

On the number of cubic orders of bounded discriminant having automorphism group C3, and related problems, with M. Bhargava,

* Algebra and Number Theory*, Vol. 8 (2014), No. 1, 53-88.

Grand orbits of integer polynomials, with M. Zieve (appendix with B. Seward), *preprint* (2010).

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Teaching

I have taught the following courses at Boston College:
MATH 1100 and MATH 1105 (Calculus), 4 courses total.

MATH 3310 (Abstract Algebra), 2 semesters.

MATH 2210 (Linear Algebra), 1 semester.

MATH 882201, An introduction to *p*-adic Hodge theory.

I taught the following classes while at Michigan:
Math 115 (Calc I), 3 semesters

Math 116 (Calc II), 2 semesters

Math 215 (Calc III), 1 semester (as Lab Instructor)