## Research

My research interests are in the field of algebraic number theory, and more specifically, arithmetic dynamics. The main focus of my research is studying how the absolute Galois group of a field acts on pre-images of a point under iterates of a rational function. This area has many nice applications to number theory and dynamics.

### Papers

J. Juul, H. Krieger, N. Looper, M. Manes, B. Thompson, and L. Walton, ``Arboreal representations for rational maps with few critical points,'' manuscript submitted for publication. Available at arXiv: 1804.06053 , 13 pages, 2018.

(preprint pdf)
R. Benedetto, J. Juul, ``Odoni's conjecture for number fields,'' manuscript submitted for publication. Available at arXiv: 1803.01987, 15 pages, 2018.

(preprint pdf)
J. Juul, ``The Image Size of Iterated Rational Maps over Finite Fields,'' Available at arXiv:1706.07458, 22 pages, 2017.

(preprint pdf)
R. Benedetto, X. Faber, B. Hutz, J. Juul, and Y. Yasufuku, ``A cubic PCF arboreal representation,'' to appear in Research in Number Theory. Available at arXiv: 1612.03358, 20 pages, 2016.

(preprint pdf)
J. Juul, ``Fixed point proportions for Galois groups of non-geometric iterated extensions,'' Available at arXiv:1603.06103, 14 pages, 2016.

(preprint pdf)
J. Juul, ``Iterates of generic polynomials and generic rational functions,'' to appear in Trans. Amer. Math. Soc. Available at arXiv: 1410.3814, 25 pages, 2016.

(preprint pdf)
A. Bridy, P. Ingram, R. Jones, J. Juul, A. Levy, M. Manes, S. Rubenstein-Salezedo, R. Rumely, and J. Silverman, ``Finite ramification for preimage fields of postcritically finite morphisms,'' to appear in Math. Res. Letters. Available at arXiv: 1511.00194, 10 pages, 2016.

(preprint pdf)
J. Juul, P. Kurlberg, K. Madhu, and T. J. Tucker, ``Wreath products and proportions of periodic points,'' Int. Math. Res. Not. IMRN, (13):3944-3969, 2016.

(preprint pdf)