Papers  

• • On the factorization of iterates of x^d+c in large degree, [arXiv] 

  • Unicritical polynomials over abc-fields: from uniform boundedness to dynamical Galois groups (with John Doyle), [arXiv]  

  • On the proportion of irreducible polynomials in unicritically generated semigroups (with R. Jacobs, B. Keller, A. Kim, P. Ye, and A. Zhou), J. Algebra, to appear. [arXiv]  

  • Dynamical diophantine approximation exponents in characteristic p, Bulletin LMS, 56.12 (2024): 3801-3818. [arXiv] 

  • Counting points by height in semigroup orbits (with J. P. Bell and X. Zhong), Canad. J. Math., to appear. [arXiv] 

  • The size of semigroup orbits modulo primes (with J. H. Silverman), Pacific J. Math., 325.2 (2023): 281-297..  [arXiv] 

  • Galois groups and prime divisors in random quadratic sequences (with J. Doyle, V. O. Healey, and R. Jones), Math. Proc. Camb. Philos. Soc, 176.1 (2024): 95-122. [arXiv] 

  • Irreducible polynomials in quadratic semigroups (with Reiyah Jacobs and Peter Ye), J. Number Theory, 248 (2023): 208-241.  [arxiv] 

  • Isotriviality, integral points, and primitive primes  in orbits in characteristic p (with A. Carney and T. J. Tucker), Algebra & Number Theory, 17.9 (2023): 1573-1594. [arXiv] 

  • Orbit counting in polarized dynamical systems, Disc. and Cont. Dynam. Syst., Ser. A, 42.1 (2022): 189-210.  [arXiv] 

  • Counting points of bounded height in monoid orbits, Math Z, 301 (2022): 3395-3416. [arXiv] 

  • Dynamical height growth: left, right, and total orbits, Pacific J. Math., 311-2 (2021): 329-367. [arXiv]  

  • Dynamical and arithmetic degrees for random iterations of maps on projective space, Math. Proc. Camb. Philos. Soc, (2021): 1-17. [arXiv]  

  • Eventually stable quadratic polynomials over ℚ (with R. Jones, M.Stoll, et. al.), New York Journal Math., 26 (2020): 526-561. [Link]   

  • Riccati equations and polynomial dynamics over function fields, (with R. Jones), Trans. Amer. Math. Soc., 373 (2020): 1555-1575. [arXiv] 

  • Finite orbit points for sets of quadratic polynomials, Int. J. Number Theory, 15.8 (2019): 1693-1719. [arXiv]        

  • Stochastic canonical heights, (with V. O. Healey), J. Number Theory, 201 (2019): 228-256. [arXiv] 

  • The average number of integral points in orbits, Math Res. Lett., 26.1 (2019): 101-120. [arXiv] 

  • Galois groups of some iterated polynomials over cyclotomic extensions, Arch. Math. (Basel), 110.2 (2018): 109–113. [arXiv] 

  • Classifying Galois groups of small iterates via rational points, Int. J. Number Theory, 14.5 (2018): 1403-1426. [arXiv] 

  • Average Zsigmondy sets, dynamical Galois groups, and the Kodaira-Spencer map, Trans. Amer. Math. Soc., 370.9 (2018): 6391–6410. [arXiv] 

  • Galois groups of iterates of some unicritical polynomials, (with M. Bush and N. Looper), Acta Arith., 181 (2017): 57-73. [arXiv] 

  • Integral points of bounded degree on the projective line and in dynamical orbits (with J. Gunther), Proc. Amer. Math Soc., 145.12 (2017): 5087-5096. [arXiv] 

  • Integrality estimates in orbits over function fields, J. Number Theory, 177 (2017): 1-19. [arXiv] 

  • Prime divisors in polynomial orbits over function fields, Bulletin LMS, 48.6 (2016): 1029-1036. [arXiv]  

  • The Vojta conjecture implies Galois rigidity in dynamical families, Proc. Amer. Math Soc., 144 (2016): 1931-1939. [arXiv] 

  • Galois uniformity in quadratic dynamics over rational function fields, J. Number Theory, 148 (2015): 372-383. [arXiv]  

  • Rational points on certain families of symmetric equations, Int. J. Number Theory, 11.6 (2015): 1821-1838. [arXiv] 

  • The Arithmetic of curves defined by iteration, Acta Arith. 169 (2015): 1-27. [arXiv] 

  • Points on elliptic curves parametrizing dynamical Galois groups, Acta Arith. 159 (2013): 149-167. [arXiv] 

Thesis

(advised by Joseph Silverman )

Galois uniformity in arithmetic dynamics, Brown University 2015.