Organizing Committee
 Matthew Baker
Georgia Institute of Technology  Rob Benedetto
Amherst College  Charles Favre
Ecole Polytechnique  Kevin Pilgrim
Indiana University  Juan RiveraLetelier
Pontificia Universidad Catolica de Chile
Abstract
This workshop will bring together researchers working in classical complex dynamics and in the newer area of padic (nonarchimedean) dynamics. It will promote interactions between the two groups by highlighting the similarities and differences between complex and padic dynamics.
In particular, it will address Berkovich space, whose introduction has greatly enhanced the exchange of ideas between complex and padic dynamics.
Confirmed Speakers & Participants
 Speaker
 Poster Presenter
 Attendee
 Virtual Attendee

Jackie Anderson
Bridgewater State University

Matthieu Arfeux
Universite de Toulouse III (Paul Sabatier)

Cecile Armana
Westfälische WilhelmsUniversität Münster

Matthew Baker
Georgia Institute of Technology

Tatiana Bandman
BarIlan University

Fabrizio Barroero
Technische Universität Graz

Eric Bedford
Indiana University

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)

Alexandru Buium
University of New Mexico

Zoe Chatzidakis
Centre National de la Recherche Scientifique (CNRS)

Arnaud Chéritat
Institut de Mathématiques de Toulouse

Mark Comerford
University of Rhode Island

Carlos D'Andrea
University of Barcelona

Laura DeMarco
University of Illinois

Kevin Doerksen
Simon Fraser University

Dzmitry Dudko
University of Goettingen

Adam Epstein
University of Warwick

Xander Faber
University of Hawaii

Youssef Fares
Universite de Picardie (Jules Verne)

Charles Favre
Ecole Polytechnique

Tatiana Firsova
Stony Brook University

Joanna Furno
University of North Carolina  Charlotte

Derek Garton
University of Wisconsin

Thomas Gauthier
Universite de Toulouse III (Paul Sabatier)

Dragos Ghioca
University of British Columbia

William Gignac
University of Michigan

Walter Gubler
Universität Regensburg

LiangChung Hsia
National Taiwan Normal University

Benjamin Hutz
Saint Louis University

Zair Ibragimov
California State University

Patrick Ingram
York University

Hiroyuki Inou
Kyoto University

Rafe Jones
College of the Holy Cross

Mattias Jonsson
University of Michigan

Jeremy Kahn
Brown University

Shu Kawaguchi
Osaka University

Tomoki Kawahira
Nagoya University

Kiran Kedlaya
University of California, San Diego

Sarah Koch
University of Michigan, Ann Arbor

Par Kurlberg
Kungliga Tekniska Hogskolan

ChongGyu Lee
University of Illinois

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

Jonathan Lubin
Brown University

Mikhail Lyubich
SUNY

Mahdi MajidiZolbanin
City College, CUNY

Michelle Manes
Mathematics Department

Nikita Miasnikov
City University of New York (CUNY)

John Milnor
SUNY

Khoa Nguyen
University of California, Berkeley

Yûsuke Okuyama
Kyoto Institute of Technology

Frank Palladino
University of Rhode Island

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

Carsten Petersen
Roskilde University Center

Kevin Pilgrim
Indiana University

Jorge Pineiro
Bronx Community College, CUNY

Lukas Pottmeyer
Universität Regensburg

Remus Radu
Stony Brook University

Juan RiveraLetelier
Pontificia Universidad Catolica de Chile

Bastien Rossetti
Universite de Toulouse III (Paul Sabatier)

Robert Rumely
University of Georgia

Adriana Salerno
Bates College

Zachary Scherr
University of Michigan

Dierk Schleicher
Jacobs University

Nikita Selinger
Jacobs University

Thomas Sharland
University of Warwick

Mitsuhiro Shishikura
Kyoto University

Joseph Silverman
Brown University

Lucien Szpiro
City University of New York (CUNY)

Raluca Tanase
Cornell University

Bianca Thompson
University of Hawaii at Manoa

Eugenio Trucco
Universidad Austral de Chile

Thomas Tucker
University of Rochester

Eva Uhre
Stony Brook University

Bianca Viray
University of Washington

Paul Vojta
University of California, Berkeley

Xiaoguang Wang
Chinese Academy of Sciences

ChiHao Wang
National Central University

Kazuhiko Yamaki
Kyoto University

Xinyi Yuan
Princeton University

Ilies Zidane
Universite de Toulouse III (Paul Sabatier)

Michael Zieve
University of Michigan
Workshop Schedule
Monday, February 13, 2012
Time  Event  Location  Materials 

8:30  8:55am EST  Registration  
8:55  9:00am EST  Welcome  Jeff Brock, Deputy Director, ICERM  11th Floor Lecture Hall  
9:00  9:45am EST  Geometry of Feigenbaum Julia sets  Mikhail Lyubich, SUNY  11th Floor Lecture Hall  
10:00  10:30am EST  Coffee/Tea Break  11th Floor Collaborative Space  
10:30  11:15am EST  Geometric Limits and Renormalization  Jeremy Kahn, Brown University  11th Floor Lecture Hall  
11:30  12:15pm EST  Special curves and post‐critically finite maps in the moduli space  Laura DeMarco, University of Illinois  11th Floor Lecture Hall  
12:30  2:30pm EST  Break for Lunch Free Time  
2:30  3:15pm EST  Quantitative Equidistribution in NonArchimedean and Complex Dynamics  Yusuke Okuyama, Kyoto Institute of Technology  11th Floor Lecture Hall  
3:30  4:00pm EST  Coffee/Tea Break  11th Floor Collaborative Space  
4:00  4:45pm EST  Strong bifurcation loci of maximal Hausdorff dimension  Thomas Gauthier, Université de Toulouse III (Paul Sabatier)  11th Floor Lecture Hall  
5:00  6:30pm EST  Welcome Reception 
Tuesday, February 14, 2012
Time  Event  Location  Materials 

9:00  9:45am EST  The Berkovich Ramification Locus  Structure and Applications  Xander Faber, University of Hawaii  11th Floor Lecture Hall  
10:00  10:30am EST  Coffee/Tea Break  11th Floor Collaborative Space  
10:30  11:15am EST  Wandering Domains in Spherically Complete Fields  Eugenio Trucco, Centro de Estudios Científicos de Santiago  11th Floor Lecture Hall  
11:30  12:15pm EST  On the nonarchimedean CalabiYau Theorem  Xinyi Yuan, Princeton University  11th Floor Lecture Hall  
12:30  2:30pm EST  Break for Lunch Free Time  
2:30  3:15pm EST  Canonical measures on subvarieties of abelian varieties  Walter Gubler, Universität Regensburg  11th Floor Lecture Hall  
3:30  4:00pm EST  Coffee/Tea Break  11th Floor Collaborative Space  
4:00  4:45pm EST  Singular metrics and the CalabiYau theorem in nonArchimedan geometry  Mattias Jonsson, University of Michigan  11th Floor Lecture Hall 
Wednesday, February 15, 2012
Thursday, February 16, 2012
Friday, February 17, 2012
Tutorial Week Schedule
Thursday, February 9, 2012
Time  Event  Location  Materials 

10:30  11:50am EST  Postcritically Finite Rational Maps and their Deformations  Jeremy Kahn, Brown University  11th Floor Lecture Hall  
2:30  3:30pm EST  Denseness of repelling cycles in the Julia set and its parameter analogue  Tomoko Kawahira, Tomoki Kawahira, Nagoya University  11th Floor Lecture Hall  
3:30  4:00pm EST  Coffee/Tea Break  11th Floor Collaborative Space  
4:00  5:00pm EST  Padic parametrization and the cyclic case of the dynamical MordellLang conjecture  Thomas Tucker, University of Rochester  11th Floor Lecture Hall 
Friday, February 10, 2012
Time  Event  Location  Materials 

11:00  12:00pm EST  Computational Working Group  11th Floor Lecture Hall  
2:30  3:30pm EST  Dynamical ManinMumford conjectures  Thomas Tucker, University of Rockester  11th Floor Lecture Hall  
3:30  4:00pm EST  Coffee/Tea Break  11th Floor Collaborative Space  
4:00  5:00pm EST  Transversality for postcritically finite rational maps  Xavier Buff, Université de Toulouse III Paul Sabatier  11th Floor Lecture Hall 
Problems
Problem 1: Potential Theory and Invariant Measures.
In the past decade, a number of researchers have developed a robust potential theory on Berkovich spaces and used it to construct an invariant measure associated to each rational map acting on Berkovich projective line, which is in some respects analog to the maximal entropy measure in complex dynamics. It is known to be ergodic and supported on the Julia set, but many fundamental questions remain.
Problem 2: Equidistribution Theorems.
Various special sets of points (periodic, preperiodic, small height, Galois conjugates, etc.) have been shown to be equidistributed with respect to the maximal entropy measure in the Riemann sphere and/or to the analog measure on Berkovich projective line. These equidistribution results have had a number of important applications. A focus of the workshop will be to formulate and prove additional equidistribution results and give further applications.
Problem 3: Dynamics of Fatou Components.
In 2000, RiveraLetelier classified the possible dynamics on periodic components of the Berkovichspace Fatou set of a rational function, a classification that is analogous to the complex results of Fatou and Julia. Many questions remain open, including bounds for the number of periodic cycles of quasiperiodicity domains and the existence of wandering Fatou domains over the padic rationals.
Problem 4: Transversality in Complex Dynamics.
Thurston's rigidity theorem gives a topological characterization of critically finite rational maps. Recent work of Epstein on an infinitesimal version of Thurston's theorem has an underlying arithmetic flavor. The workshop will provide an opportunity to explore these powerful new analytic/algebraic tools for studying both complex and padic dynamics.
Problem 5: The Local Connectivity Conjecture.
This longstanding and fundamental conjecture asserts that the Mandelbrot set is locally connected. Its resolution would have major implications, including the density of hyperbolic maps in moduli space. Might there be tools from arithmetic dynamics which could be useful for studying this fundamental conjecture?