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

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 12-2pm

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

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.

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, Pre-images of quadratic dynamical systems, forthcoming, Involve, Vol 4. (2011), no. 4, 343-363.

1. 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

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), 637-660.

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

7. Benjamin Hutz, Trevor Hyde, and Benjamin Krause, Pre-images of quadratic dynamical systems, forthcoming in Involve, Vol 4. (2011), no. 4, 343-363.

6. Xander Faber, Benjamin Hutz, and Michael Stoll, Pre-images of the origin: on the number of rational iterated pre-images of the origin under quadratic dynamical systems, International Journal of Number Theory, 7 (2011), no. 7, 1781-1806

Magma script - preimages.magma

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

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

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

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, 1109-1126

1. 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 (2009), no. 1, 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, in preparation.


Mathematics Links
Florida Tech Department of Mathematical Sciences
Sage - mathematical software
Sage-dynamics

 

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