Benjamin Hutz

Assistant Professor

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Office: 308D

E-mail: bhutz (at) fit (dot) edu

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Florida Institue of Technology
Department of Mathematical Sciences
150 W. University Blvd
Melbourne, Florida 32901
Phone (321) 674-8091
Fax (321) 674-7412

CV

me

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)

Tuesday 3:30-5:00pm
Thursday 12:30-2:00pm
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

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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

all of my papers on arXiv

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