Research

Research Interests

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

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)