Organizing Committee
Abstract

This workshop will present topics in low-dimensional dynamics such as billiards, flows on flat surfaces, dynamics on moduli spaces, and piecewise isometric maps. One theme in the workshop will be the appearance of geometric structures such as hyperbolic space and Teichmüller space in connection with dynamical systems which are basically defined in terms of the Euclidean plane. Computer experiments are common in these areas, and will be discussed, but the emphasis will be on the mathematics that comes out of the experiments.

Image for "Geometric Structures in Low-Dimensional Dynamics"

Confirmed Speakers & Participants

Talks will be presented virtually or in-person as indicated in the schedule below.

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Workshop Schedule

Monday, November 18, 2013
TimeEventLocationMaterials
8:30 - 8:55am ESTWorkshop Registration11th Floor Collaborative Space 
8:55 - 9:00am ESTWelcome - ICERM Director11th Floor Lecture Hall  
9:00 - 9:50am ESTPolytope Exchanges as compactifications - Richard Schwartz, Brown University11th Floor Lecture Hall
10:00 - 10:30am ESTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20am ESTCutting and resewing pillow cases - Patrick Hooper, City College, CUNY11th Floor Lecture Hall
11:30 - 12:20pm ESTAverage cusp excursions and random walks on the mapping class group - Giulio Tiozzo, Harvard University11th Floor Lecture Hall
12:30 - 2:30pm ESTBreak for Lunch and Free Time  
2:30 - 3:20pm ESTNear-integrable behavior in a system with discrete phase space - Heather Reeve-Black and Franco Vivaldi, Queen Mary, University of London11th Floor Lecture Hall
3:30 - 4:00pm ESTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:50pm ESTRenormalization of a one-parameter family of piece-wise isometries - John Lowenstein, New York University11th Floor Lecture Hall
5:00 - 6:30pm ESTWelcome Reception11th Floor Collaborative Space 
Tuesday, November 19, 2013
TimeEventLocationMaterials
9:00 - 9:50am ESTDiagonal changes on translation surfaces - Corinna Ulcigrai, University of Bristol11th Floor Lecture Hall
10:00 - 10:30am ESTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20am ESTWeak-mixing for billiards in regular polygons - Vincent Delecroix, Universite de Paris VII (Denis Diderot)11th Floor Lecture Hall
11:30 - 12:20pm ESTOn the ergodicity of billiards in non-rational polygons - Giovanni Forni, University of Maryland11th Floor Lecture Hall
12:30 - 2:30pm ESTBreak for Lunch and Free Time  
2:30 - 3:20pm ESTMinimal and not uniquely ergodic interval exchange transformations - Jon Chaika, University of Chicago11th Floor Lecture Hall
3:30 - 4:00pm ESTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:50pm ESTDynamics on Panov planes and applications - Martin Schmoll, Clemson University11th Floor Lecture Hall
Wednesday, November 20, 2013
TimeEventLocationMaterials
9:00 - 10:00am ESTTeichmüller curves and theta functions - Martin Möller, Johann Wolfgang Goethe-Universität Frankfurt11th Floor Lecture Hall
10:00 - 10:30am ESTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:30am ESTFiniteness of Teichmueller curves in genus three - Matthew Bainbridge, Indiana University11th Floor Lecture Hall
11:30 - 12:30pm ESTIsoperiodic forms in genus 2: fake pentagons and snow falling on cedars - Curtis McMullen, Harvard University11th Floor Lecture Hall 
12:30 - 12:40pm ESTGroup Photo in Lecture HallLecture Hall 
12:40 - 2:30pm ESTBreak for Lunch and Free Time  
2:30 - 3:20pm ESTGL(2,R) orbit closures of translation surfaces - Alexander Wright, University of Chicago11th Floor Lecture Hall
3:30 - 4:00pm ESTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:50pm ESTHodge theory and rigidity for Teichmuller dynamics - Simion Filip, University of Chicago11th Floor Lecture Hall
7:00 - 8:30pm ESTPoster Session and Dessert Reception11th Floor Lecture Hall and Collaborative Space 
Thursday, November 21, 2013
TimeEventLocationMaterials
9:00 - 9:50am ESTFiniteness results for Teichmueller curves in Prym loci - Erwan Lanneau, Université de Grenoble I (Joseph Fourier)11th Floor Lecture Hall
10:00 - 10:30am ESTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20am ESTThe Kontsevich-Zorich cocycle over certain cyclic covers - Carlos Matheus Silva Santos, Université de Paris XIII (Paris-Nord)11th Floor Lecture Hall 
11:30 - 12:20pm ESTHorocycle invariant measures in the moduli space of translation surfaces - Barak Weiss, Tel Aviv University11th Floor Lecture Hall
12:30 - 2:30pm ESTBreak for Lunch and Free Time  
2:30 - 3:20pm ESTFrom tiling and packing to uniformization via combinatorial harmonic maps - Sa’ar Hersonsky, University of Georgia11th Floor Lecture Hall 
3:30 - 4:00pm ESTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:50pm ESTUsing dynamics to construct surface groups - Ursula Hamenstaedt, Rheinische Friedrich-Wilhelms-Universität Bonn11th Floor Lecture Hall
Friday, November 22, 2013
TimeEventLocationMaterials
9:00 - 9:50am ESTCutting sequences on Bouw-Moller surfaces - Diana Davis, Northwestern University11th Floor Lecture Hall
10:00 - 10:30am ESTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:20am ESTHurwitz translation surfaces - Gabriela Weitze-Schmithuessen, Karlsruhe Institute of Technology11th Floor Lecture Hall
11:30 - 12:20pm ESTExplicit algebraic models for Teichmuller curves via Hilbert modular forms - Ronen Mukamel, University of Chicago11th Floor Lecture Hall 
12:30 - 12:40pm ESTICERM Long Term Visitor Group PhotoLecture Hall 
12:30 - 2:30pm ESTBreak for Lunch and Free Time  
2:30 - 3:20pm ESTThe SL(2,R) action on moduli space - Alex Eskin, University of Chicago11th Floor Lecture Hall
3:30 - 4:00pm ESTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:50pm ESTA construction of non-uniquely ergodic measured laminations - Kasra Rafi, University of Toronto11th Floor Lecture Hall

Tutorial Week Schedule

Thursday, November 14, 2013
TimeEventLocationMaterials
10:30 - 11:50am ESTTopics in geometric structures - Rich Schwartz, Brown University11th Floor Lecture Hall 
2:30 - 4:00pm ESTWorkshop Tutorial Session I: Introducing polygonal inner and outer billiards - Sergei Tabachnikov, Pennsylvania State University11th Floor Lecture Hall 
4:00 - 4:30pm ESTCoffee Break11th Floor Collaborative Space 
Friday, November 15, 2013
TimeEventLocationMaterials
10:00 - 11:30am ESTWorkshop Tutorial Session II: Finding closed geodesics on rational billiard tables - John Smillie, Cornell University11th Floor Lecture Hall 
2:00 - 3:30pm ESTWorkshop Tutorial Session III: Counting and the Siegel-Veech Machine - Jayadev Athreya, University of Illinois at Urbana-Champaign11th Floor Lecture Hall 
3:30 - 4:00pm ESTCoffee Break11th Floor Collaborative Space 
4:00 - 5:00pm ESTPresentation of SAGE11th Floor Lecture Hall 

Associated Semester Workshops

Low-dimensional Topology, Geometry, and Dynamics
Image for "Low-dimensional Topology, Geometry, and Dynamics"
Sep 9 - Dec 6, 2013
Semester Program
Exotic Geometric Structures
Image for "Exotic Geometric Structures"
Sep 15 - 20, 2013
Semester Workshop

Lecture Videos

The SL(2,R) action on moduli space

Alex Eskin
University of Chicago
November 22, 2013
Geometric Structures in Low-Dimensional Dynamics
Play     Abstract

Hurwitz translation surfaces

Gabriella Weitze-Schmithuesen
Karlsruhe Institute of Technology
November 22, 2013
Geometric Structures in Low-Dimensional Dynamics
Play     Abstract

Cutting sequences on Bouw-Moller surfaces

Diana Davis
Northwestern University
November 22, 2013
Geometric Structures in Low-Dimensional Dynamics
Play     Abstract

From tiling and packing to uniformization via combinatorial harmonic maps

Sa'ar Hersonsky
University of Georgia
November 21, 2013
Geometric Structures in Low-Dimensional Dynamics
Play     Abstract

Horocycle invariant measures in the moduli space of translation surfaces

Barak Weiss
Tel Aviv University
November 21, 2013
Geometric Structures in Low-Dimensional Dynamics
Play     Abstract

Hodge theory and rigidity for Teichmuller dynamics

Simion Filip
University of Chicago
November 20, 2013
Geometric Structures in Low-Dimensional Dynamics
Play     Abstract

GL(2,R) orbit closures of translation surfaces

Alexander Wright
University of Chicago
November 20, 2013
Geometric Structures in Low-Dimensional Dynamics
Play     Abstract

Isoperiodic forms in genus 2 - fake pentagons and snow falling on cedars

Curtis McMullen
Harvard University
November 20, 2013
Geometric Structures in Low-Dimensional Dynamics
Play

Teichmüller curves and theta functions

Martin Möller
Goethe-Universitat Frankfurt
November 20, 2013
Geometric Structures in Low-Dimensional Dynamics
Play     Abstract

On the ergodicity of billiards in non-rational polygons

Giovanni Forni
University of Maryland
November 19, 2013
Geometric Structures in Low-Dimensional Dynamics
Play     Abstract

Weak-mixing for billiards in regular polygons

Vincent Delecroix
CNRS
November 19, 2013
Geometric Structures in Low-Dimensional Dynamics
Play     Abstract

Diagonal changes on translation surfaces

Corinna Ulcigrai
University of Bristol
November 19, 2013
Geometric Structures in Low-Dimensional Dynamics
Play     Abstract

Renormalization of a one-parameter family of piece-wise isometries

John Lowenstein
New York University
November 18, 2013
Geometric Structures in Low-Dimensional Dynamics
Play     Abstract

Average cusp excursions and random walks on the mapping class group

Giulio Tiozzo
Yale University
November 18, 2013
Geometric Structures in Low-Dimensional Dynamics
Play     Abstract

Cutting and resewing pillow cases

Patrick Hooper
City College, CUNY
November 18, 2013
Geometric Structures in Low-Dimensional Dynamics
Play     Abstract

Polytope Exchanges as compactifications

Richard Schwartz
Brown University
November 18, 2013
Geometric Structures in Low-Dimensional Dynamics
Play     Abstract