## Benjamin HutzAssistant Professor ------------------------------------------------------ Office: 308D E-mail: bhutz (at) fit (dot) edu ------------------------------------------------------- Florida Institue of Technology |

**Teaching Schedule**

Fall 2014

Multivariable
Caclulus, Math 2001 Section 2

Multivariable Caclulus, Math 2001 Section E1

Complex Analysis, Math 3101

Office Hours (in Crawford 308D)

tbd

or by appointment.

Florida Tech now has a sage server available for math student research projects. Contact me for an account on the server.

**Sage-Dynamics: Software for computation and
experimentation in dynamical systems for Sage**

This project is partially supported by NSF grant DMS-1415294.

Sage-dynamics - 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 - research statement.

**Student Research**

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**

1. Sonia
Seetermado, *Failure of Thurston transverality modulo primes.*

2. Dillon Rose and Weixin Wu, Computer Science Senior Design Project:
*Sage-dynamics*.

3. Joao de Faria and Benjamin Hutz, *Combinatorics of cycle lengths on
Wehler K3 surfaces over finite fields*, 10 pages, arXiv:1309.6598.

4. Benjamin Hutz, Trevor Hyde, and Benjamin Krause, *Pre-images of quadratic
dynamical systems*, Involve, 4:4 (2011), 343-363.

5. Trevor Hyde, *On the number of pre-images of -1 under quadratic dynamical
systems*, American Journal of Undergraduate Research, 9:1 (2010), 19-26.

**Publications and Preprints**

1. Joao de Faria
and Benjamin Hutz, *Combinatorics of cycle lengths on Wehler K3 Surfaces
over finite field*, 10 pages, arXiv:1309.6598., submitted.

2. Benjamin Hutz and Adam Towsley, *Thurston's Theorem and Misiurewicz
points for polynomial maps*, 10 pages, arXiv:1309.4048, submitted.

3. Benjamin Hutz and Michelle Manes, *The Field of Definition for Dynamical
Systems on PN*, Bulletin of the Institute of Mathematics Academia Sinica,
10 pages, forthcoming.

4. Benjamin Hutz, *Determination of all rational preperiodic points for
morphisms of PN*, Mathematics of Computation, 18 pages, forthcoming

5. 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

6. Benjamin Hutz and Lucien Szpiro, *Almost newton, sometimes lattes,*
Journal of Number Theory 136 (2013), 423-437.

7. 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 QQ - rational.c

C code QQ(sqrt(5)) - disc5.c

8. Robert L.
Benedetto, Dragos Ghioca, Benjamin Hutz, Par Kurlberg, Thomas Scanlon, and
Thomas J. Tucker, *Periods of rational maps modulo primes*,
Mathematische Annalen, 355:2 (2013), 637-660.

9. Benjamin Hutz, *Effectivity of dynatomic cycles for morphisms of
projective varieties using deformation theory*, Proceedings of the AMS, 140
(2012), 3507-3514.

10. Benjamin Hutz, Trevor Hyde, and Benjamin Krause, *Pre-images of
quadratic dynamical systems*, Involve, 4:4 (2011), 343-363.

11. Xander Faber, Benjamin Hutz, and Michael Stoll, *Pre-images of the
origin: on the number of rational iterated pre-images of the origin under
quadratc dynamical systems*, International Journal of Number Theory, 7:7
(2011), 1781-1806

Magma script - preimages.magma

12. Benjamin Hutz,
*Dynatomic cycles for morphisms of projective varieties*, New York
Journal of Mathematics 16 (2010) 125-159

13. Benjamin Hutz, *Rational periodic points for degree two polynomial
morphisms on projective space*, Acta Arithmetica 141 (2010) 275-288

14. Benjamin Hutz, *A computational investigation of Wehler K3
surfaces*, New Zealand Journal of Mathematics, 39 (2009) 133-141

Pari/gp script - ordersearch.gp

15. Benjamin Hutz,
*Good reduction of periodic points on projecctive varieties*, Illinois
Journal of Mathematics 53:4 (Winter 2009), 1109-1126

16. Xander Faber, Benjamin Hutz, Patrick Ingram, Rafe Jones, Michelle Manes,
Thomas J. Tucker, and Michael E. Zieve, *Uniform bounds on pre-images under
quadratic polynomials*, Mathematical Research Letters 16:1 (2009),
87-101.

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*, submitted to
publisher.

Mathematics Links |

Florida Tech Department of Mathematical Sciences |

Sage - mathematical software |

Sage-dynamics |

Other Links |

Space Coast Crew |

Beachside TriSport |

Pet Partners (Therapy Dogs) |

Indian River Dog Training Club |

Last Updated 7/6/2014