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.

Fractal food: Chou Romanesco.

Confirmed Speakers & Participants

Workshop Schedule

Monday, March 7, 2016
TimeEventLocationMaterials
8:30 - 8:55Registration11th Floor Collaborative Space 
8:55 - 9:00Welcome - ICERM Director11th Floor Lecture Hall 
9:00 - 9:45Entropies on covers of compact manifolds - Francois Ledrappier, University of Notre Dame Paris11th Floor Lecture Hall
10:00 - 10:45Prime number theorems and holonomies for hyperbolic rational maps - Hee Oh, Yale University11th Floor Lecture Hall
11:00 - 11:30Coffee/Tea Break11th Floor Collaborative Space 
11:30 - 12:15New developments in smooth rigidity of lattice actions. - Federico Rodriguez Hertz, PSU11th Floor Lecture Hall
12:30 - 2:30Break for Lunch / Free Time  
2:30 - 3:15Thurston eigenvalues- a spectral gap - Sarah Koch, University of Michigan, Ann Arbor11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45Continuity of core entropy of quadratic polynomials - Giulio Tiozzo, Yale University11th Floor Lecture Hall
5:00 - 6:30Welcome Reception11th Floor Collaborative Space 
Tuesday, March 8, 2016
TimeEventLocationMaterials
9:00 - 9:45Non-differentiability points for topological conjugaicies of countable branch Markov maps - Thomas Jordan, University of Bristol11th Floor Lecture Hall
10:00 - 10:45Non-uniform hyperbolicity, symbolic dynamics, and applications - Yuri Lima, University of Paris-Sud11th Floor Lecture Hall
11:00 - 11:30Coffee/Tea Break11th Floor Collaborative Space 
11:30 - 12:15Finiteness of measures maximizing the entropy for surface diffeomorphisms - Sylvain Crovisier, University of Paris11th Floor Lecture Hall
12:30 - 12:40Group Photo in Lecture Hall11th Floor Lecture Hall 
12:40 - 2:30Break for Lunch / Free Time  
2:30 - 3:15Non-uniform specification properties, thermodynamic formalism, and towers - Vaughn Climenhaga, University of Houston11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45Unique equilibrium states for geodesic flows in nonpositive curvature - Todd Fisher, Brigham Young University11th Floor Lecture Hall
Wednesday, March 9, 2016
TimeEventLocationMaterials
9:00 - 9:45Criteria for zero averages and applications in partially hyperbolic dynamics. - Lorenzo Diaz, Pontifical Catholic University of Rio de Janeiro11th Floor Lecture Hall
10:00 - 10:45Skeletons for transitive fibered maps - Katrin Gelfert, Federal University of Rio de Janeiro (UFRJ)11th Floor Lecture Hall
11:00 - 11:30Coffee/Tea Break11th Floor Collaborative Space 
11:30 - 12:15Universality of the large deviation principle in one-dimensional dynamics - Yong Moo Chung, Hiroshima University11th Floor Lecture Hall
12:30 - 2:30Break for Lunch / Free Time - 11th Floor Lecture Hall 
2:30 - 3:15Decay of correlations in fast-slow partially hyperbolic systems - Jacopo de Simoi, University of Toronto11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45Martingale 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 - 9:45Quantum chaos and the thermodynamical formalism - Stephane Nonnenmacher, Université Paris-sud11th Floor Lecture Hall
10:00 - 10:45Spectral gaps via additive combinatorics - Semyon Dyatlov, MIT11th Floor Lecture Hall
11:00 - 11:30Coffee/Tea Break11th Floor Collaborative Space 
11:30 - 12:15The spectrum of semi-classical transfer operator for expanding semi-flows with holes. - Masato Tsujii, Kyushu University11th Floor Lecture Hall
12:30 - 2:30Break for Lunch / Free Time - 11th Floor Lecture Hall 
2:30 - 3:15Fourier transforms of measures on the Brownian graph - Jonathan Fraser, University of Manchester11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 
4:00 - 4:45Multifractal 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 - 9:45Computation and inverse problems for linear response. - Mark Pollicott, University of Warwick11th Floor Lecture Hall
10:00 - 10:45On the fractal geometry of horseshoes in arbitrary dimensions - Carlos Gustavo Moreira, IMPA11th Floor Lecture Hall
11:00 - 11:30Coffee/Tea Break11th Floor Collaborative Space 
11:30 - 12:15New 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 - 1:15Sums of Cantor sets and convolutions of singular measures - Anton Gorodetski, University of California, Irvine11th Floor Lecture Hall
1:30 - 3:15Break for Lunch / Free Time - 11th Floor Lecture Hall 
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space 

Associated Semester Workshops

Dimension and Dynamics
Computation in Dynamics

Lecture Videos

Skeletons for transitive fibered maps

Katrin Gelfert
Federal University of Rio de Janeiro (UFRJ)
March 9, 2016