Benjamin HutzAssistant Professor  Office: 308D Email: bhutz (at) fit (dot) edu  Florida Institue of Technology Department of Mathematical Sciences 150 W. University Blvd Melbourne, Florida 32901 Phone (321) 6748091 Fax (321) 6747412

Teaching Schedule
Spring 2013
Multivariable Caclulus, Math 2001 Section 1
Multivariable Caclulus, Math 2001 Section E1
Algebra/Group Theory, Math 4051/5050
Office Hours (in Crawford 308D)
Wed 122pm
or by appointment.
Florida Tech now has a sage server available for math student research projects. Contact me for an account on the server.
SageDynamics: Software for computation and experimentation in dynamical systems for Sage
Sagedynamics  main page for status and information on the project
Some examples using the functionality:
ICERM Workshop 2: slides ; Sage examples
ICERM Beginning of semester problems: Sage worksheet
Computational Records in Algebraic Dynamics
Research Interests
Arithmetic dynamics,number theory, and associated computational problems.
Student Reserach
If you are interested in problems in the area of iterated functions (dynamical systems) and developping software in Sage to work with these problems, then stop by my office.
I have projects ranging from theoretical problems to computational experimentation to implementation of algorithms. Problems are appropriate for students with mathematical and/or programming (python or C) backgrounds of all levels.
Previous projects
3. Joao de Faria and Benjamin Hutz, Combinatorics of cycle lengths on Wehler K3 Surfaces over finite field, 10 pages, arXiv:1309.6598.
2. Benjamin Hutz, Trevor Hyde, and Benjamin Krause, Preimages of quadratic dynamical systems, forthcoming, Involve, Vol 4. (2011), no. 4, 343363.
1. Trevor Hyde, On the number of preimages of 1 under quadratic dynamical systems, American Journal of Undergraduate Research, 9:1 (2010), 1926.
Publications and preprints
18. Benjamin Hutz and Michelle Manes, Invariant theory and automorphism groups, in progress.
17. Benjamin Hutz, Computing canonical heights and rational preperiodic points over number fields, in progress.
16. Joao de Faria and Benjamin Hutz, Combinatorics of cycle lengths on Wehler K3 Surfaces over finite field, 10 pages, arXiv:1309.6598.
15. Benjamin Hutz and Adam Towsley, Thurston's Theorem and Misiurewicz points for polynomial maps, 10 pages, arXiv:1309.4048, submitted.
14. Benjamin Hutz and Michelle Manes, The field of definition for dynamical systems on P^N, 10 pages, arXiv:1309.6696, submitted.
13. Benjamin Hutz and Lucien Szpiro, Almost newton, sometimes lattes, 11 pages  Journal of Number Theory, forthcoming, arXiv:1105.1696,
12. Benjamin Hutz, Determination of all rational preperiodic points for morphisms of PN, Mathematics of Computation, 18 pages, forthcoming
11. Benjamin Hutz and Michael Tepper, Multiplier Spectra and the Moduli Space of Degree 3 Morphisms on P1, JP Journal of Algebra, Number Theory and Applications, 10 pages, forthcoming
10. Benjamin Hutz, Patrick Ingram, On Poonen's conjecture concerning rational preperiodic points of quadratic maps, forthcoming in Rocky Mountain Journal of Mathematics, 9 pages  arXiv:0909.5050
C code for Q  rational.c
C code Q(sqrt(5))  disc5.c
9. Robert L. Benedetto, Dragos Ghioca, Benjamin Hutz, Par Kurlberg, Thomas Scanlon, and Thomas J. Tucker, Periods of rational maps modulo primes, forthcoming Mathematische Annalen, 355:2 (2013), 637660.
8. Benjamin Hutz, Effectivity of dynatomic cycles for morphisms of projective varieties using deformation theory, forthcoming in Proceedings of the AMS, 140 (2012), 35073514.
7. Benjamin Hutz, Trevor Hyde, and Benjamin Krause, Preimages of quadratic dynamical systems, forthcoming in Involve, Vol 4. (2011), no. 4, 343363.
6. Xander Faber, Benjamin Hutz, and Michael Stoll, Preimages of the origin: on the number of rational iterated preimages of the origin under quadratic dynamical systems, International Journal of Number Theory, 7 (2011), no. 7, 17811806
Magma script  preimages.magma
5. Benjamin Hutz, Dynatomic cycles for morphisms of projective varieties, New York Journal of Mathematics 16 (2010) 125159
4. Benjamin Hutz, Rational periodic points for degree two polynomial morphisms on projective space, Acta Arithmetica 141 (2010) 275288
3. Benjamin Hutz, A computational investigation of Wehler K3 surfaces, New Zealand Journal of Mathematics, 39 (2009) 133141
Pari/gp script  ordersearch.gp
2. Benjamin Hutz, Good reduction of periodic points on projecctive varieties, Illinois Journal of Mathematics 53 (Winter 2009), no. 4, 11091126
1. Xander Faber, Benjamin Hutz, Patrick Ingram, Rafe Jones, Michelle Manes, Thomas J. Tucker, and Michael E. Zieve, Uniform bounds on preimages under quadratic polynomials, Mathematical Research Letters 16 (2009), no. 1, 87101.
Thesis: Arithmetic Dynamics on Varieties of Dimension Greater Than One, 2007
Advisor: Joseph Silverman, Brown University
Entire thesis (214
pages)
Introduction
only (17 pages)
Books
1. Benjamin Hutz, An Experimental Introduction to Number Theory, in preparation.
Mathematics Links

Florida Tech Department of Mathematical Sciences 
Sage  mathematical software 
Sagedynamics 
Other Links

Space Coast Crew 
Space Coast Multisport 
Pet Partners (Therapy Dogs) 
Indian River Dog Training Club 