Research Interests

I am a student of Joe Silverman, and I primarily work on questions at the intersection of dynamical systems and number theory.


Mathematics Publications


R. Jones and M. Manes.
"Galois theory of quadratic rational functions."


Paper on ArXiv


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


Paper on ArXiv


E. 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, Amer. Math. Soc., Providence, RI, 2011, pp. 237–247.




E. Malmskog and M. Manes.
"Almost divisibility in the Ihara zeta functions of certain ramified covers of $q+1$-regular graphs."
Journal of Linear Algebra and 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 (2009) 87 – 101.


Paper on ArXiv


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


Paper on ArXiv


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




Many of the papers above are available on arXiv, though they may differ slightly from the final, published version. (My arXiv papers are here.) Most of my thesis appears in the last two papers listed above. If you want the whole original for some reason (errors and all), you can find it here.


Projects in Progress


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