Organizing Committee
- Matthew Baker
Georgia Institute of Technology - Rob Benedetto
Amherst College - Charles Favre
Ecole Polytechnique - Kevin Pilgrim
Indiana University - Juan Rivera-Letelier
Pontificia Universidad Catolica de Chile
Abstract
This workshop will bring together researchers working in classical complex dynamics and in the newer area of p-adic (nonarchimedean) dynamics. It will promote interactions between the two groups by highlighting the similarities and differences between complex and p-adic dynamics.
In particular, it will address Berkovich space, whose introduction has greatly enhanced the exchange of ideas between complex and p-adic dynamics.
Confirmed Speakers & Participants
Talks will be presented virtually or in-person as indicated in the schedule below.
- Speaker
- Poster Presenter
- Attendee
- Virtual Attendee
-
Jackie Anderson
Bridgewater State University
-
Matthieu Arfeux
Universite de Toulouse III (Paul Sabatier)
-
Cecile Armana
Westfälische Wilhelms-Universität Münster
-
Matthew Baker
Georgia Institute of Technology
-
Tatiana Bandman
Bar-Ilan 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
-
Liang-Chung 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
-
Jan-Li Lin
Indiana University
-
Karl-Olof Lindahl
Linnaeus University
-
Sijun Liu
University of Michigan
-
Jonathan Lubin
Brown University
-
Mikhail Lyubich
SUNY
-
Mahdi Majidi-Zolbanin
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 Rivera-Letelier
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
-
Chi-Hao 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 Non-Archimedean 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 non-archimedean Calabi--Yau 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 Calabi-Yau theorem in non-Archimedan 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 | P-adic parametrization and the cyclic case of the dynamical Mordell-Lang 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 Manin-Mumford 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, Rivera-Letelier classified the possible dynamics on periodic components of the Berkovich-space 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 p-adic 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 p-adic 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?