Organizing Committee
Abstract

A surprising discovery of 20th century mathematics is that many deterministic systems exhibit random behavior. One early example of a chaotic system was Lorenz equation used by meteorologist Edward Lorenz as a simplified model of atmospheric convection. One of the most common mechanisms of stochasticity is the Smale horseshoe appearing near a homoclinic intersection.

The Lorentz attractor and Smale horseshoe are typical examples of fractal invariant sets for dynamical systems. Fractal objects are ubiquitous in dynamics, including invariant sets, invariant measures, invariant foliations et cetera.

Thermodynamical formalism is a powerful tool for studying dimensions of fractal objects. It originated in statistical mechanics, but currently it has applications to many areas of mathematics including spectral theory, hyperbolic geometry and probability theory.

The goal of this conference is to bring together experts studying fractal objects in dynamics in order to review recent progress in the field and catalyze further research.

Image for "Fractal Geometry, Hyperbolic Dynamics and Thermodynamical Formalism"
Fractal food: Chou Romanesco.

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, March 7, 2016
TimeEventLocationMaterials
8:30 - 8:55am ESTRegistration11th Floor Collaborative Space 
8:55 - 9:00am ESTWelcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:45am ESTEntropies on covers of compact manifolds - Francois Ledrappier, University of Notre Dame Paris11th Floor Lecture Hall
10:00 - 10:45am ESTPrime number theorems and holonomies for hyperbolic rational maps - Hee Oh, Yale University11th Floor Lecture Hall
11:00 - 11:30am ESTCoffee/Tea Break11th Floor Collaborative Space 
11:30 - 12:15pm ESTNew developments in smooth rigidity of lattice actions. - Federico Rodriguez Hertz, PSU11th Floor Lecture Hall
12:30 - 2:30pm ESTBreak for Lunch / Free Time  
2:30 - 3:15pm ESTThurston eigenvalues- a spectral gap - Sarah Koch, University of Michigan, Ann Arbor11th Floor Lecture Hall
3:30 - 4:00pm ESTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45pm ESTContinuity of core entropy of quadratic polynomials - Giulio Tiozzo, Yale University11th Floor Lecture Hall
5:00 - 6:30pm ESTWelcome Reception11th Floor Collaborative Space 
Tuesday, March 8, 2016
TimeEventLocationMaterials
9:00 - 9:45am ESTNon-differentiability points for topological conjugaicies of countable branch Markov maps - Thomas Jordan, University of Bristol11th Floor Lecture Hall
10:00 - 10:45am ESTNon-uniform hyperbolicity, symbolic dynamics, and applications - Yuri Lima, University of Paris-Sud11th Floor Lecture Hall
11:00 - 11:30am ESTCoffee/Tea Break11th Floor Collaborative Space 
11:30 - 12:15pm ESTFiniteness of measures maximizing the entropy for surface diffeomorphisms - Sylvain Crovisier, University of Paris11th Floor Lecture Hall
12:30 - 12:40pm ESTGroup Photo in Lecture Hall11th Floor Lecture Hall 
12:40 - 2:30pm ESTBreak for Lunch / Free Time  
2:30 - 3:15pm ESTNon-uniform specification properties, thermodynamic formalism, and towers - Vaughn Climenhaga, University of Houston11th Floor Lecture Hall
3:30 - 4:00pm ESTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45pm ESTUnique equilibrium states for geodesic flows in nonpositive curvature - Todd Fisher, Brigham Young University11th Floor Lecture Hall
Wednesday, March 9, 2016
TimeEventLocationMaterials
9:00 - 9:45am ESTCriteria for zero averages and applications in partially hyperbolic dynamics. - Lorenzo Diaz, Pontifical Catholic University of Rio de Janeiro11th Floor Lecture Hall
10:00 - 10:45am ESTSkeletons for transitive fibered maps - Katrin Gelfert, Federal University of Rio de Janeiro (UFRJ)11th Floor Lecture Hall
11:00 - 11:30am ESTCoffee/Tea Break11th Floor Collaborative Space 
11:30 - 12:15pm ESTUniversality of the large deviation principle in one-dimensional dynamics - Yong Moo Chung, Hiroshima University11th Floor Lecture Hall
12:30 - 2:30pm ESTBreak for Lunch / Free Time - 11th Floor Lecture Hall 
2:30 - 3:15pm ESTDecay of correlations in fast-slow partially hyperbolic systems - Jacopo de Simoi, University of Toronto11th Floor Lecture Hall
3:30 - 4:00pm ESTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45pm ESTMartingale methods in the study of almost everywhere convergence of ergodic series - Ai-Hua Fan, Université de Picardie Jules Verne11th Floor Lecture Hall
Thursday, March 10, 2016
TimeEventLocationMaterials
9:00 - 9:45am ESTQuantum chaos and the thermodynamical formalism - Stephane Nonnenmacher, Université Paris-sud11th Floor Lecture Hall
10:00 - 10:45am ESTSpectral gaps via additive combinatorics - Semyon Dyatlov, MIT11th Floor Lecture Hall
11:00 - 11:30am ESTCoffee/Tea Break11th Floor Collaborative Space 
11:30 - 12:15pm ESTThe spectrum of semi-classical transfer operator for expanding semi-flows with holes. - Masato Tsujii, Kyushu University11th Floor Lecture Hall
12:30 - 2:30pm ESTBreak for Lunch / Free Time - 11th Floor Lecture Hall 
2:30 - 3:15pm ESTFourier transforms of measures on the Brownian graph - Jonathan Fraser, University of Manchester11th Floor Lecture Hall
3:30 - 4:00pm ESTCoffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45pm ESTMultifractal analysis of some families of random functions motivated by the study of the network traffic - Karoly Simon, Budapest University of Technology and Economics11th Floor Lecture Hall
Friday, March 11, 2016
TimeEventLocationMaterials
9:00 - 9:45am ESTComputation and inverse problems for linear response. - Mark Pollicott, University of Warwick11th Floor Lecture Hall
10:00 - 10:45am ESTOn the fractal geometry of horseshoes in arbitrary dimensions - Carlos Gustavo Moreira, IMPA11th Floor Lecture Hall
11:00 - 11:30am ESTCoffee/Tea Break11th Floor Collaborative Space 
11:30 - 12:15pm ESTNew criteria for equality of Hausdorff and affinity dimensions, via self-affine measures on positive subsystems - Pablo Shmerkin, Torcuato Di Tella University11th Floor Lecture Hall
12:30 - 1:15pm ESTSums of Cantor sets and convolutions of singular measures - Anton Gorodetski, University of California, Irvine11th Floor Lecture Hall
1:30 - 3:15pm ESTBreak for Lunch / Free Time - 11th Floor Lecture Hall 
3:30 - 4:00pm ESTCoffee/Tea Break11th Floor Collaborative Space 

Associated Semester Workshops

Dimension and Dynamics
Image for "Dimension and Dynamics"
Feb 1 - May 6, 2016
Semester Program
Computation in Dynamics
Image for "Computation in Dynamics"
Apr 4 - 8, 2016
Semester Workshop

Lecture Videos

Sums of Cantor sets and convolutions of singular measures

Anton Gorodetski
University of California Irvine
March 11, 2016
Fractal Geometry, Hyperbolic Dynamics and Thermodynamical Formalism
Play     Abstract

New criteria for equality of Hausdorff and affinity dimensions, via self-affine measures on positive subsystems

Pablo Shmerkin
Torcuato Di Tella University
March 11, 2016
Fractal Geometry, Hyperbolic Dynamics and Thermodynamical Formalism
Play     Abstract

On the fractal geometry of horseshoes in arbitrary dimensions

Carlos Moreira
Instituto Nacional de Matemática Pura e Aplicada (IMPA)
March 11, 2016
Fractal Geometry, Hyperbolic Dynamics and Thermodynamical Formalism
Play     Abstract

Computation and inverse problems for linear response.

Mark Pollicott
Warwick University
March 11, 2016
Fractal Geometry, Hyperbolic Dynamics and Thermodynamical Formalism
Play     Abstract

Multifractal analysis of some families of random functions motivated by the study of the network traffic

Karoly Simon
Budapest University of Technology and Economics
March 10, 2016
Fractal Geometry, Hyperbolic Dynamics and Thermodynamical Formalism
Play     Abstract

Fourier transforms of measures on the Brownian graph

Jonathan Fraser
University of Manchester
March 10, 2016
Fractal Geometry, Hyperbolic Dynamics and Thermodynamical Formalism
Play     Abstract     Slides

The spectrum of semi-classical transfer operator for expanding semi-flows with holes

Masato Tsujii
Kyushu University
March 10, 2016
Fractal Geometry, Hyperbolic Dynamics and Thermodynamical Formalism
Play     Abstract

Quantum chaos and the thermodynamical formalism

Stéphane Nonnenmacher
Université Paris-sud
March 10, 2016
Fractal Geometry, Hyperbolic Dynamics and Thermodynamical Formalism
Play     Abstract     Slides

Martingale methods in the study of almost everywhere convergence of ergodic series

Ai-Hua Fan
Université de Picardie Jules Verne
March 9, 2016
Fractal Geometry, Hyperbolic Dynamics and Thermodynamical Formalism
Play     Abstract

Decay of correlations in fast-slow partially hyperbolic systems

Jacopo de Simoi
University of Toronto
March 9, 2016
Fractal Geometry, Hyperbolic Dynamics and Thermodynamical Formalism
Play     Abstract

Universality of the large deviation principle in one-dimensional dynamics

Yong Moo Chung
Hiroshima University
March 9, 2016
Fractal Geometry, Hyperbolic Dynamics and Thermodynamical Formalism
Play     Abstract     Slides

Skeletons for transitive fibered maps

Katrin Gelfert
Universidade Federal do Rio de Janerio
March 9, 2016
Fractal Geometry, Hyperbolic Dynamics and Thermodynamical Formalism
Play     Abstract     Slides

Criteria for zero averages and applications in partially hyperbolic dynamics

Lorenzo Diaz
Pontifical Catholic University of Rio de Janeiro
March 9, 2016
Fractal Geometry, Hyperbolic Dynamics and Thermodynamical Formalism
Play     Abstract

Unique equilibrium states for geodesic flows in nonpositive curvature

Todd Fisher
Brigham Young University
March 8, 2016
Fractal Geometry, Hyperbolic Dynamics and Thermodynamical Formalism
Play     Abstract     Slides

Non-uniform specification properties, thermodynamic formalism, and towers

Vaughn Climenhaga
University of Houston
March 8, 2016
Fractal Geometry, Hyperbolic Dynamics and Thermodynamical Formalism
Play     Abstract

Finiteness of measures maximizing the entropy for surface diffeomorphisms

Sylvain Crovisier
University of Paris - Sud
March 8, 2016
Fractal Geometry, Hyperbolic Dynamics and Thermodynamical Formalism
Play     Abstract

Non-uniform hyperbolicity, symbolic dynamics, and applications

Yuri Lima
Universite Paris-Sud 11
March 8, 2016
Fractal Geometry, Hyperbolic Dynamics and Thermodynamical Formalism
Play     Abstract

Non-differentiability points for topological conjugaicies of countable branch Markov maps

Thomas Jordan
University of Bristol
March 8, 2016
Fractal Geometry, Hyperbolic Dynamics and Thermodynamical Formalism
Play     Abstract

Continuity of core entropy of quadratic polynomials

Giulio Tiozzo
Yale University
March 7, 2016
Fractal Geometry, Hyperbolic Dynamics and Thermodynamical Formalism
Play     Abstract

New developments in smooth rigidity of lattice actions.

Federico Rodriguez Hertz
PSU
March 7, 2016
Fractal Geometry, Hyperbolic Dynamics and Thermodynamical Formalism
Play     Abstract

Entropies on covers of compact manifolds

Francois Ledrappier
University of Notre Dame
March 7, 2016
Fractal Geometry, Hyperbolic Dynamics and Thermodynamical Formalism
Play     Abstract