Research Interests

You can find most of my mathematics papers on arXiv.

Mathematics Publications


M. Manes, and J.H. Silverman.
"A classification of degree 2 semi-stable rational maps P2P2 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."



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 PN."
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.



Most of my thesis appears in the last two papers listed above. The original thesis is here.


Selected Eduation Publications


M. Manes.
"Mathematics for Elementary Teachers"
Open Education Resource (2013).


Mathematics for Elementary Teachers I.
Mathematics for Elementary Teachers II.
Instructors' Guide.


M. Manes.
"Building Bridges between Universities and K – 12 Schools."
Notes of the Canadian Mathematical Society, 42.5 (Oct/Nov 2010), 8 – 9.


Paper available online.


M. Manes.
Learning Math: Geometry.
Annenberg CPB (2003).
Multimedia online geometry course for teachers of grades K – 8.


Online course.


Education Development Center (one of four lead authors)
IMPACT Mathematics.
Glencoe, McGraw Hill.
Middle school program focused on algebra for all students.


Publisher website.


A. Cuoco and M. Manes.
"When Memory Fails: Putting Limitations to Good Use."
Mathematics Teacher 94.6 (2001), 489 – 493.



M. Manes.
"A special case of the isoperimetric problem."
Mathematics Teacher 91.2 (1998), 100.



P. Frorer, O. Hazzan, and M. Manes.
"Revealing the Faces of Abstraction."
International Journal for Computers in Mathematics Learning 2.3 (1997), 217 – 228.



M. Manes.
"Technology Tips: A Global Electronic Community."
Mathematics Teacher 87.8 (1994), 650 – 651.



mmanes home