Organizing Committee
 Xander Faber
University of Hawaii  Michelle Manes
Mathematics Department  Lucien Szpiro
City University of New York (CUNY)  Thomas Tucker
University of Rochester  Michael Zieve
University of Michigan
Abstract
This workshop will examine global arithmetic dynamics from the perspectives of number theory, algebraic geometry, and model theory. It will introduce aspects of this topic to a larger audience, and clarify connections between different perspectives. In addition, there will be extensive discussion periods in which participants can collaborate on theoretical and computational aspects of the topic.
Confirmed Speakers & Participants

Domenico Aiello
University of Massachusetts

Ekaterina Amerik
Universite de Paris XI (ParisSud)

Jackie Anderson
Bridgewater State University

Matthieu Arfeux
Universite de Toulouse III (Paul Sabatier)

Cecile Armana
Westfälische WilhelmsUniversität Münster

Fabrizio Barroero
University of Basel

Rob Benedetto
Amherst College

Anupam Bhatnagar
City University of New York (CUNY)

Araceli Bonifant
University of Rhode Island

Andrew Bridy
University of Wisconsin

Xavier Buff
Universite de Toulouse III (Paul Sabatier)

Frederic Campana
Université de Nancy I (Henri Poincaré)

Jung Kyu Canci
Universität Basel

Zoe Chatzidakis
Centre National de la Recherche Scientifique (CNRS)

Laura DeMarco
Northwestern University

John Doyle
University of Georgia

Dzmitry Dudko
University of Goettingen

Noam Elkies
Harvard University

Adam Epstein
University of Warwick

Xander Faber
University of Hawaii

Paul Fili
Oklahoma State University

Tanya Firsova
Kansas State University

Derek Garton
University of Wisconsin

William Gignac
University of Michigan

Chad Gratton
University of Rochester

Wade Hindes
The Graduate Center, CUNY

LiangChung Hsia
National Taiwan Normal University

Hsiu Lien Huang
Academia Sinica

Benjamin Hutz
Saint Louis University

Suion Ih
University of Colorado at Boulder

Patrick Ingram
York University

Jeremy Kahn
Brown University

Sarah Koch
University of Michigan, Ann Arbor

Holly Krieger
MIT

Par Kurlberg
Kungliga Tekniska Hogskolan

ChongGyu Lee
University of Illinois

Benjamin LeVeque
Brown University

Aaron Levin
Michigan State University

Alon Levy
Institute for Computational and Experimental Research in Mathematics (ICERM)

Huaibin Li
Pontificia Universidad Catolica de Chile

JanLi Lin
Indiana University

KarlOlof Lindahl
Linnaeus University

Sijun Liu
University of Michigan

Michelle Manes
Mathematics Department

Alice Medvedev
City College, CUNY

Ricardo Menares
Pontificia Universidad Catolica de Chile

John Milnor
SUNY

Igor Minevich
Brown University

Khoa Nguyen
University of California, Berkeley

Andrew Obus
University of Virginia

Alina Ostafe
Macquarie University

Frank Palladino
University of Rhode Island

Donghoon Park
Korea Advanced Institute of Science and Technology (KAIST)

Jorge Pineiro
Bronx Community College, CUNY

Bjorn Poonen
MIT

Lukas Pottmeyer
Universität Regensburg

Jamie Rahr
University of Rochester

Juan RiveraLetelier
Pontificia Universidad Catolica de Chile

John Roberts
University of New South Wales

Robert Rumely
University of Georgia

Thomas Scanlon
University of California, Berkeley

Zachary Scherr
University of Michigan

Dierk Schleicher
Jacobs University

Thomas Sharland
University of Warwick

Joseph Silverman
Brown University

Martin Sombra
Universitat de Barcelona

William Stein
University of Washington

Michael Stoll
Universität Bayreuth

Brian Stout
City University of New York (CUNY)

Lucien Szpiro
City University of New York (CUNY)

Michael Tepper
Pennsylvania State University, Ogontz Campus

Lubos Thoma
University of Rhode Island

Bianca Thompson
University of Hawaii at Manoa

Adam Towsley
University of Rochester

Thomas Tucker
University of Rochester

Bianca Viray
University of Washington

Paul Vojta
University of California, Berkeley

Jose Voloch
University of Canterbury

ChiHao Wang
National Central University

Xiaoguang Wang
Chinese Academy of Sciences

Lloyd West
City University of New York (CUNY)

Siman Wong
Department of Mathematics & Statistics

Elizabeth Wulcan
Chalmers University of Technology

Kazuhiko Yamaki
Kyoto University

Yu Yasufuku
Nihon University

Tianjun Ye
Georgia Tech College of Computing

ShouWu Zhang
Princeton University

Liang Zhao
City University of New York (CUNY)

Michael Zieve
University of Michigan
Workshop Schedule
Monday, March 19, 2012
Tuesday, March 20, 2012
Time  Event  Location  Materials 

9:00  9:50  Adelic intersection problems in arithmetic geometry and dynamics  Felipe Voloch, University of Texas at Austin  11th Floor Lecture Hall  
9:55  10:20  Coffee/Tea Break  11th Floor Collaborative Space  
10:20  11:00  Simple and Critically Good Reduction For Endomorphisms of P1  Jung Kyu Canci, University of Basel  11th Floor Lecture Hall  
11:05  11:55  Using Sage for Mathematical Research  William Stein, University of Washington  11th Floor Lecture Hall  
11:55  12:00  Group Photo  11th Floor Lecture Hall  
12:00  1:45  Break for Lunch & Free Time  
1:45  5:00  Problem Session and Collaborative Work/Coffee & Tea Break  11th Floor Collaborative Space  
7:00  10:00  Hackathon  10th Floor Collaborative Space 
Wednesday, March 21, 2012
Time  Event  Location  Materials 

9:00  9:50  Dynamical exponential and transcendence  ShouWu Zhang, Princeton University  11th Floor Lecture Hall  
9:55  10:20  Coffee/Tea Break  11th Floor Collaborative Space  
10:20  11:00  Good reduction and computational applications  Benjamin Hutz, CUNY Graduate Center  11th Floor Lecture Hall  
11:05  11:55  Iteration of algebraic points under a rational selfmap  Ekaterina Amerik, Higher School of Economics (Moscow) and Universite ParisSud (Orsay)  11th Floor Lecture Hall  
12:00  1:45  Break for Lunch & Free Time  
1:45  5:00  Progress Reports and Collaborative Work/Coffee & Tea Break  11th Floor Collaborative Space  
7:00  9:00  Poster Session and Dessert Reception  11th Floor Lecture Hall 
Thursday, March 22, 2012
Time  Event  Location  Materials 

9:00  9:50  TBA  Tom Scanlon, University of California, Berkeley  11th Floor Lecture Hall  
9:55  10:20  Coffee/Tea Break  11th Floor Collaborative Space  
10:20  11:10  Algebraic Dynamics Difference Fields and Model Theory  Zoe Chatzidakis, Université de Paris VII (Denis Diderot)  11th Floor Lecture Hall  
11:15  11:55  A property of integral division points on curves and its dynamical system analogue  SuIon Ih, University of Colorado  11th Floor Lecture Hall  
11:55  12:00  Survey Distribution, please return to 11th floor reception desk  
12:00  1:45  Break for Lunch & Free Time  
1:45  2:35  On the (failure of) equidistribution of periodic points  Juan RiveraLetelier, Pontificia Universidad Catolica de Chile  11th Floor Lecture Hall  
2:35  5:00  Progress Reports and Collaborative Work/Coffee & Tea Break  11th Floor Collaborative Space  
7:00  10:00  Hackathon  10th Floor Collaborative Space 
Friday, March 23, 2012
Tutorial Week Schedule
Monday, March 12, 2012
Time  Event  Location  Materials 

2:30  3:30  Fields with several automorphisms  Alice Medvedev, UC Berkeley  11th Floor Lecture Hall  
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space  
4:00  5:00  The dynamics of birational maps over finite fields and their signatures  John A. G. Roberts, The University of New South Wales, Sydney, Australia  11th Floor Lecture Hall 
Tuesday, March 13, 2012
Time  Event  Location  Materials 

10:30  11:50  Postcritically Finite Rational Maps and their Deformations  Jeremy Kahn, Brown University  11th Floor Lecture Hall  
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space  
4:00  5:00  Professional Development: Ethics in research I  11th Floor Lecture Hall 
Wednesday, March 14, 2012
Time  Event  Location  Materials 

3:14  4:00  Coffee/Tea Break and Pi Day Treats!  11th Floor Collaborative Space  
4:00  5:00  Postdoc/Grad Student Seminar  11th Floor Lecture Hall 
Thursday, March 15, 2012
Time  Event  Location  Materials 

10:30  11:50  Postcritically Finite Rational Maps and their Deformations  Jeremy Kahn, Brown University  11th Floor Lecture Hall  
1:30  2:30  Introduction to Height Functions  Yu Yasufuku, Nihon University  11th Floor Lecture Hall  
2:30  3:00  Coffee/Tea Break  11th Floor Collaborative Space  
3:00  4:00  Modeltheoretic properties for algebraic dynamics, via ACFA  Alice Medvedev, UC Berkeley  11th Floor Lecture Hall 
Friday, March 16, 2012
Time  Event  Location  Materials 

11:00  12:00  Computational Working Group/Seminar  11th Floor Lecture Hall  
2:30  3:30  Equidistribution of small points on $\mathbb{P}^1$  Juan RiveraLetelier, Pontificia Universidad Catolica de Chile  11th Floor Lecture Hall  
3:30  4:00  Coffee/Tea Break  11th Floor Collaborative Space 
Problems
Problem 1: The Uniform Boundedness Conjecture.
This fundamental conjecture in arithmetic dynamics says that for given positive integers D, n, and d with d>1, if K/Q is a number field of degree D and if f:Pn→Pn is a morphism of degree d defined over K, then the number of Krational preperiodic points of f is bounded by a constant depending only on D, n, and d. It is a vast generalization of the MazurMerel theorem on uniform boundedness of torsion points on elliptic curves.
Problem 2: Dynamical Intersection Theorems.
Two fundamental arithmetic results for abelian varieties are theorems of Raynaud and Faltings, orginally formulated as conjectures by ManinMumford and MordellLang, respectively. There are a number of dynamical analogues of these conjectures, which roughly say that the orbit of a point should intersect a subvariety only finitely often unless the orbit of the entire subvariety has special properties. Only special cases of the dynamical conjectures have been proven. We expect these problems to be a major focus of the workshop.
Problem 3: Global Applications of Equidistribution Theorems.
Let (xi) be a of sequence of algebraic points whose fcanonical heights go to zero. Under suitable hypotheses, it is known that the Galois conjugates of the xi are equidistributed with respect to the complex and Berkovich invariant measures. A focus of the program will be on global arithmetic applications of this and other similar equidistribution theorems.
Problem 4: Arithmetic Dynamics Over Function Fields.
Many theorems in arithmetic geometry were first proven in the easier setting of function fields. A theme for the workshop will be the analogy for arithmetic dynamics between number fields and function fields.
Problem 5: LocalGlobal Problems.
There are many localglobal principles in arithmetic geometry, such as those related to the Hasse and BrauerManin obstructions. The workshop will explore analogous localglobal principles for dynamical systems, including especially the distribution of orbits modulo primes and/or in padic or complex neighborhoods.