Benjamin Hutz - Amherst College Department of Mathematics and Computer Science

Home Teaching Research CV

Arithmetic Dynamical Systems, Number Theory, and Algebraic Geometry

Research Statement

Publications and Preprints
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.
Benjamin Hutz, "Rational periodic points for degree two polynomial morphisms on projective space" forthcoming in Acta Arithmetica - arXiv:0811.3225
Benjamin Hutz, "Good Reduction of Periodic Points on Projecctive Varieties"
forthcoming in Illinois Journal of Mathematics- arXiv:0801.3645
"Pre-images of the Origin: On the Number of Rational Iterated Pre-images of the Origin Under Quadratic Dynamical Systems" submitted - arXiv:0810.1715

Benjamin Hutz, "Dynatomic Cycles for Morphisms of Projective Varieties"

submitted - arXiv:0801.3643
Benjamin Hutz, "A Computational Investigation of Wehler K3 Surfaces"
submitted - arXiv:0801.3648
Pari/gp script - ordersearch.gp
Benjamin Hutz, Patrick Ingram, "Numerical evidence for a conjecture of Poonen"

in preparation
C code for Q - rational.c
C code Q(sqrt(5)) - disc5.c

Thesis:
Arithmetic Dynamics on Varieties of Dimension Greater Than One, 2005
Advisor:
Joseph Silverman, Brown University
Entire thesis (214 pages)
Introduction only (17 pages)

all of my papers on arXiv

Conferences
Bellairs Workshop: Moduli Spaces and the Arithmetic of Dynamical Systems, May 2010 Invited
AMS/MAA Joint Meeting, January 2010 Speaker
Special Session: Arithmetic and Nonarchimedean Dynamics
Maine/Quebec Number Theory Conference October 2009 Speaker - slides
AMS Central Section Meeting at UIUC, March 2009 Speaker - slides
Special Session on the Interface Between Number Theory and Dynamical Systems

Banff Internation Research Station: Arithmetic of K3 Surfaces
11/30-12/5/09

Invited
American Institute of Mathetmatics: Uniform Boundedness Conjecture
1/14-1/18/2008
Invited
Arizona Winter School 2007: p-adic Geometry
Berkovic Space project (with Matt Baker)
MAA Northeastern Sectional Meeting Spring 2006
Speaker
Arizona Winter School 2006: Computational and Algorithmic Aspects of Algebra and Arithmetic

Cohomological Dimensions of the Normal Bundle for Certain Classes of Monomial Ideals (with Michael Stillman)

A Macaulay2 script to generate random shellable complexes by taking randomly generated posets. shellable.m2

AMS/MAA National Conference 2006
Midwest Number Theory Conference for Graduate Students IV Fall 2006
Speaker
Workshop in p-adic Dynamics: Weslyan University 5/14-5/16/2005
AMS/MAA National Conference 2003

 

Seminars
Five College Number Theory Seminar - Fall 2007
Dynatomic Cycles
Brown Graduate Student Seminar Fall 2006
What is a Groebner Basis?
MAA Northeastern Sectional Meeting Spring 2006
Arithmetic Dynamics on a class of K3 surfaces
Brown Graduate Student Seminar Spring 2005
Mazur's Thoerem
Brown Graduate Student Seminar Spring Fall 2004
Godel's Proof
Brown Graduate Student Seminar Spring 2004
Gauss Sums

 

Presentation Slides and Other Notes
Background for Mazur's Theorem on Elliptic Curve Torsion
Using Jocabi Sums to count solutions to certain diophantine equations
Godel's Undecidability Proof
Enriques-Kodaira Classification of Compact Complex Surfaces