Organizing Committee
- Laura DeMarco
University of Illinois - Adam Epstein
University of Warwick - Sarah Koch
University of Michigan, Ann Arbor - Curtis McMullen
Harvard University - Joseph Silverman
Brown University
Abstract
This workshop will bring together dynamicists, number theorists, and algebraic geometers to study the geometry and arithmetic of dynamical moduli spaces. The set Ratdn of rational degree d self-maps of Pn has a natural structure as an affine variety. The dynamical moduli space Mdn is the quotient of Ratdn by the conjugation action of the group PGLn+1. Problems to be investigated include the geometry of Mdn, the distribution of special maps such as post-critically finite maps in Mdn, dynamical modular curves associated to one-parameter families of maps with a marked point of period N, and degeneration of families of maps and the associated points on the boundary of moduli space. A tutorial session will be held the week before this workshop.

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
-
Matthieu Astorg
Universite de Toulouse III (Paul Sabatier)
-
Fabrizio Barroero
Technische Universität Graz
-
Rob Benedetto
Amherst College
-
Anupam Bhatnagar
City University of New York (CUNY)
-
Paul Blanchard
Boston University
-
Araceli Bonifant
University of Rhode Island
-
Joshua Bowman
Smith College
-
Andrew Bridy
University of Wisconsin
-
Xavier Buff
Universite de Toulouse III (Paul Sabatier)
-
Arnaud Chéritat
Institut de Mathématiques de Toulouse
-
Mark Comerford
University of Rhode Island
-
Daniel Cuzzocreo
Boston University
-
Diana Davis
Northwestern University
-
Laura DeMarco
University of Illinois
-
Romain Dujardin
Ecole Polytechnique
-
Adam Epstein
University of Warwick
-
Timo Erkama
University of Eastern Finland
-
Derek Garton
University of Wisconsin
-
Jonah Gaster
University of Illinois
-
William Gignac
University of Michigan
-
Mikhail Hlushchanka
Jacobs University
-
Wei Ho
Columbia University
-
Liang-Chung Hsia
National Taiwan Normal University
-
John Hubbard
Cornell University
-
Benjamin Hutz
Saint Louis University
-
Patrick Ingram
York University
-
Rafe Jones
College of the Holy Cross
-
Jeremy Kahn
Brown University
-
Linda Keen
Herbert H. Lehman College, CUNY
-
Jan Kiwi
Pontificia Universidad Catolica de Chile
-
Sarah Koch
University of Michigan, Ann Arbor
-
Janne Kool
Universiteit Utrecht
-
Robert Kozma
Stony Brook University
-
ChongGyu Lee
University of Illinois
-
Tan Lei
Universite d'Angers
-
Alon Levy
Institute for Computational and Experimental Research in Mathematics (ICERM)
-
Huaibin Li
Pontificia Universidad Catolica de Chile
-
Jan-Li Lin
Indiana University
-
Kathryn Lindsey
University of Chicago
-
Jinsong Liu
Chinese Academy of Sciences
-
Khudoyor Mamayusupov
Jacobs University
-
Michelle Manes
Mathematics Department
-
John Milnor
SUNY
-
Khoa Nguyen
University of California, Berkeley
-
Frank Palladino
University of Rhode Island
-
Kevin Pilgrim
Indiana University
-
Jorge Pineiro
Bronx Community College, CUNY
-
Bjorn Poonen
MIT
-
Remus Radu
Stony Brook University
-
Paul Reschke
University of Illinois at Urbana-Champaign
-
Juan Rivera-Letelier
Pontificia Universidad Catolica de Chile
-
Bastien Rossetti
Universite de Toulouse III (Paul Sabatier)
-
Robert Rumely
University of Georgia
-
Zachary Scherr
University of Michigan
-
Dierk Schleicher
Jacobs University
-
Nikita Selinger
Jacobs University
-
Thomas Sharland
University of Warwick
-
Joseph Silverman
Brown University
-
Brian Stout
City University of New York (CUNY)
-
Scott Sutherland
Stony Brook University
-
Lucien Szpiro
City University of New York (CUNY)
-
Raluca Tanase
Cornell University
-
Michael Tepper
Pennsylvania State University, Ogontz Campus
-
Bianca Thompson
University of Hawaii at Manoa
-
Thomas Tucker
University of Rochester
-
Eva Uhre
Stony Brook University
-
Bianca Viray
University of Washington
-
Paul Vojta
University of California, Berkeley
-
Chi-Hao Wang
National Central University
-
Xiaoguang Wang
Chinese Academy of Sciences
-
Hexi Ye
University of Illinois
-
Ilies Zidane
Universite de Toulouse III (Paul Sabatier)
-
Michael Zieve
University of Michigan
Workshop Schedule
Monday, April 16, 2012
Tuesday, April 17, 2012
Wednesday, April 18, 2012
Thursday, April 19, 2012
Friday, April 20, 2012
Tutorial Week Schedule
Thursday, April 12, 2012
Time | Event | Location | Materials |
---|---|---|---|
10:30 - 11:50am EDT | Postcritically Finite Rational Maps and their Deformations - Jeremy Kahn, Brown University | 11th Floor Lecture Hall | |
1:30 - 2:30pm EDT | Applications and Examples of using a new program `Dynamics Explorer' to study the dynamics of complex mappings - Suzanne Boyd, University of Wisconsin and Brian Boyd | 11th Floor Lecture Hall | |
2:30 - 2:45pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space | |
2:45 - 3:45pm EDT | Applications and Examples of using a new program `Dynamics Explorer' to study the dynamics of complex mappings - Suzanne Boyd, University of Wisconsin and Brian Boyd | 11th Floor Lecture Hall | |
4:00 - 4:30pm EDT | Sir John Ball "Smooth topology-preserving approximations of rough domains" Reception | 11th Floor Collaborative Space | |
4:30 - 5:30pm EDT | Special Colloquium-Smooth topology-preserving approximations of rough domains - Sir John Ball, University of Oxford | 11th Floor Lecture Hall |
Friday, April 13, 2012
Time | Event | Location | Materials |
---|---|---|---|
10:00 - 11:00am EDT | Moduli spaces: drawing pictures and doing computations I - Sarah Koch, Harvard University and Xavier Buff, Université de Toulouse III (Paul Sabatier) | 11th Floor Lecture Hall | |
11:30 - 12:30pm EDT | Moduli spaces: drawing pictures and doing computations II - Sarah Koch, Harvard University and Xavier Buff, Université de Toulouse III (Paul Sabatier) | 11th Floor Lecture Hall | |
2:30 - 3:30pm EDT | Computational Working Group | 11th Floor Lecture Hall | |
3:30 - 4:00pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Problems
Problem 1: The Geometry of Mdn.
It is known that M21 is isomorphic to the affine plane and that Md1 is a rational variety, but many fundamental questions remain. A major goal of the workshop will be to study the geometry of Mdn and the associated moduli spaces in which one adds level structure, for example by adding a marked point of period N or a marked finite orbit of order N. A motivating question is whether the resulting varieties are of general type if N is sufficiently large.
Problem 2: Distribution of Special Points.
An example of the type of problem to be considered is the distribution of post-critically finite maps in the moduli space Md1 in both the complex and the p-adic topologies.
Problem 3: Dynamical Modular Curves.
A one-parameter family of maps, for example fc(z)=z2+c, with marked points or orbits of order N, yields dynamical modular curves X0(N) and X1(N) that are analogous to classical modular curves. A good deal is known about the geometry of these curves, but little has been proven about their arithmetic except for some small values of N. The arithmetic properties of X0(N) and X1(N) are closely related to the uniform boundedness conjecture for the families that they parameterize.
Problem 4: The Boundary of Moduli Space.
The boundary of a moduli space and a natural method for completing the space are of fundamental importance in understanding the underlying objects and their degenerations. Recent work of Kiwi has used Berkovich space dynamics over Laurent series fields to analyze degenerations of complex dynamical systems. A goal of the workshop is to exploit these non-archimedean methods to answer classical questions about the boundary of dynamical moduli spaces over the complex numbers.