Research Interests

M. Manes, and J.H. Silverman.
"A classification of degree 2 semi-stable rational maps P² → P² with large finite dynamical automorphism group."
(Forthcoming in Annales de la Faculte des Sciences de Toulouse.)

A. Bridy, P. Ingram, R. Jones, J. Juul, A. Levy, M. Manes, S. Rubinstein-Salzedo, and J.H. Silverman.
"Finite ramification for preimage fields of postcritically finite morphisms."
(Forthcoming in Mathematical Research Letters.)

J. Anderson, I. Bouw, O. Edjer, N. Girgin, V. Karemaker, and M. Manes.
"Dynamical Belyi maps."
(Forthcoming in Women in Numbers Europe 2, Springer (2018).)

B. Thompson and M. Manes.
"Periodic points in towers of finite fields for polynomials associated to algebraic groups."
(Submitted.)

F. Balestrieri, J. Berg, M. Manes, J. Park, and B. Viray.
"Insufficiency of the Brauer-Manin obstruction for Enriques surfaces."
In Directions in Number Theory: Proceedings of the 2014 WIN3 Workshop, Springer (2016): 1–31.

I. Bouw, J. Cooley, K. Lauter, E. Lorenzo Garcia, M. Manes, R. Newton, and E. Ozman.
"Bad reduction of genus-3 curves with complex multiplication."
In Women in Numbers Europe, Springer (2015): 109–151.

X. Faber, M. Manes, and B. Viray.
"Computing conjugating sets and automorphism groups of rational functions."
J. Algebra 423 (2015): 1161–1190.

B. Hutz and M. Manes.
"The field of definition for dynamical systems on P^N."
Bull. Inst. Math. Acad. Sin. 9 (2014): 585–601.

D. Lukas, M. Manes, and D. Yap.
"A census of quadratic post-critically finite rational functions defined over Q."
LMS J. Comput. Math. 17 (2014): 314–329.

A. Levy, M. Manes, and B. Thompson.
"Uniform bounds for pre-periodic points in families of twists."
Proceedings of the AMS. 142 (2014): 3075–3088.

M.-J. Bertin, A. Feaver, J. Fuselier, M. Lalín, and M. Manes.
"Mahler measure of some singular K3-surfaces."
In Women in Numbers 2: Research Directions in Number Theory, Contemporary Mathematics, vol. 606, (2013): 237–247.

R. Jones and M. Manes.
"Galois theory of quadratic rational functions."
Commentarii Mathematici Helvetici 89 (2014): 173–213.

M. Manes and Y. Yasufuku.
"Explicit descriptions of quadratic maps on P¹ defined over a field K."
Acta Arithmetica 148 (2011), 257–267.

B. Malmskog and M. Manes.
"Ramified Covers of Graphs and the Ihara Zeta Functions of Certain Ramified Covers."
WIN — Women in Numbers , Fields Institute Communications, vol. 60 (2011): 237–247.

B. Malmskog and M. Manes.
"Almost divisibility in the Ihara zeta functions of certain ramified covers of q+1-regular graphs."
Linear Algebra and its Applications 432 (2010), 2486 – 2506.

X. Faber, B. Hutz, P. Ingram, R. Jones, M. Manes, T. Tucker, and M. Zieve.
"Uniform bounds on pre-images under quadratic dynamical systems."
Mathematical Research Letters 16.1 (2009) 87 – 101.

M. Manes.
"Moduli spaces for families of rational maps on P¹."
Journal of Number Theory 129 (2009), 1623 – 1663.

M. Manes.
"Q-rational cycles for degree-2 rational maps having an automorphism."
Proceedings of the London Mathematical Society 96 (2008), 669–696.