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.
R.L. Benedetto, D. Ghioca, J. Juul, T.J. Tucker, ``Specializations of iterated Galois groups of PCF rational functions,'' submitted for publication. (preprint pdf).
J. Juul, ``Backward Orbits of Critical Points,'' J. Number Theory (2024), https://doi.org/10.1016/j.jnt.2023.09.006. (preprint pdf).
J. Juul, H. Krieger, N. Looper, N.M. Mavraki, ``A Dynamical Shafarevich theorem for endomorphism of P^N,'' to appear Proc. Amer. Math. Soc. (preprint pdf)
J. Juul, ``The Image Size of Iterated Rational Maps over Finite Fields,'' Int. Math. Res. Not. IMRN. (2021), no. 5, 3362-3388. (preprint pdf)
J. Juul, H. Krieger, N. Looper, M. Manes, B. Thompson, and L. Walton, ``Arboreal representations for rational maps with few critical points,'' Research Directions in Number Theory: Women in Numbers IV (Association for Women in Mathematics Series, 19). (preprint pdf)
R.L. Benedetto, J. Juul, ``Odoni's conjecture for number fields,'' B. London Math. Soc. 51 (2019), no. 2, 237-250 (preprint pdf)
J. Juul. ``Iterates of generic polynomials and generic rational functions.'' Trans. Amer. Math. Soc. 371 (2019), no. 2, 809-831. (preprint pdf)
J. Juul, ``Fixed point proportions for Galois groups of non-geometric iterated extensions,'' Acta Arith. 183 (2018), no. 4, 301-315. (preprint pdf)
R.L. Benedetto, X. Faber, B. Hutz, J. Juul, and Y. Yasufuku, ``A cubic PCF arboreal representation,'' Res. Number Theory 3 (2017), 3:29. (preprint pdf)
A. Bridy, P. Ingram, R. Jones, J. Juul, A. Levy, M. Manes, S. Rubenstein-Salezedo, R. Rumely, and J.H. Silverman, ``Finite ramification for preimage fields of postcritically finite morphisms,'' Math. Res. Letters, Vol. 24, No. 6 (2017), pp. 1633-1647. (preprint pdf)
J. Juul, P. Kurlberg, K. Madhu, and T. J. Tucker, ``Wreath products and proportions of periodic points,'' Int. Math. Res. Not. IMRN (2016), no. 13, 3944-3969. (preprint pdf)