Fractal Geometry, Hyperbolic Dynamics and Thermodynamical Formalism
(March 7-11, 2016)

Picture
Fractal food: Chou Romanesco.

Description

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.

Organizing Committee

  • Lorenzo Diaz
    (Pontifical Catholic University of Rio de Janeiro)
  • Dmitry Dolgopyat
    (University of Maryland)
  • Maarit Jarvenpaa
    (University of Oulu)
  • Joerg Schmeling
    (Lund Institute of Technology)
  • Masato Tsujii
    (Kyushu University)
  • Amie Wilkinson
    (University of Chicago)

= speaker   = poster presenter

Monday March 7, 2016
Time Description Speaker Location Abstracts Slides
8:30 - 8:55Registration11th Floor Collaborative Space
8:55 - 9:00WelcomeICERM Director11th Floor Lecture Hall
9:00 - 9:45Entropies on covers of compact manifoldsFrancois Ledrappier, University of Notre Dame Paris11th Floor Lecture Hall
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10:00 - 10:45Prime number theorems and holonomies for hyperbolic rational mapsHee Oh, Yale University11th Floor Lecture Hall
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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
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12:30 - 2:30Break for Lunch / Free Time
2:30 - 3:15Thurston eigenvalues- a spectral gapSarah Koch, University of Michigan, Ann Arbor11th Floor Lecture Hall
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3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 4:45Continuity of core entropy of quadratic polynomialsGiulio Tiozzo, Yale University11th Floor Lecture Hall
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5:00 - 6:30Welcome Reception11th Floor Collaborative Space

Tuesday March 8, 2016
Time Description Speaker Location Abstracts Slides
9:00 - 9:45Non-differentiability points for topological conjugaicies of countable branch Markov mapsThomas Jordan, University of Bristol11th Floor Lecture Hall
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10:00 - 10:45Non-uniform hyperbolicity, symbolic dynamics, and applicationsYuri Lima, University of Paris-Sud11th Floor Lecture Hall
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11:00 - 11:30Coffee/Tea Break11th Floor Collaborative Space
11:30 - 12:15Finiteness of measures maximizing the entropy for surface diffeomorphismsSylvain Crovisier, University of Paris11th Floor Lecture Hall
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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 towersVaughn Climenhaga, University of Houston11th Floor Lecture Hall
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3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 4:45Unique equilibrium states for geodesic flows in nonpositive curvatureTodd Fisher, Brigham Young University11th Floor Lecture Hall
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Wednesday March 9, 2016
Time Description Speaker Location Abstracts Slides
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
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10:00 - 10:45Skeletons for transitive fibered mapsKatrin Gelfert, Federal University of Rio de Janeiro (UFRJ)11th Floor Lecture Hall
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11:00 - 11:30Coffee/Tea Break11th Floor Collaborative Space
11:30 - 12:15Universality of the large deviation principle in one-dimensional dynamicsYong Moo Chung, Hiroshima University11th Floor Lecture Hall
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12:30 - 2:30Break for Lunch / Free Time 11th Floor Lecture Hall
2:30 - 3:15Decay of correlations in fast-slow partially hyperbolic systemsJacopo de Simoi, University of Toronto11th Floor Lecture Hall
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3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space
4:00 - 4:45Martingale methods in the study of almost everywhere convergence of ergodic seriesAi-Hua Fan, Université de Picardie Jules Verne11th Floor Lecture Hall
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Thursday March 10, 2016
Time Description Speaker Location Abstracts Slides
9:00 - 9:45Quantum chaos and the thermodynamical formalismStephane Nonnenmacher, Université Paris-sud11th Floor Lecture Hall
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10:00 - 10:45Spectral gaps via additive combinatoricsSemyon Dyatlov, MIT11th Floor Lecture Hall
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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
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12:30 - 2:30Break for Lunch / Free Time 11th Floor Lecture Hall
2:30 - 3:15Fourier transforms of measures on the Brownian graphJonathan Fraser, University of Manchester11th Floor Lecture Hall
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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 trafficKaroly Simon, Budapest University of Technology and Economics11th Floor Lecture Hall
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Friday March 11, 2016
Time Description Speaker Location Abstracts Slides
9:00 - 9:45Computation and inverse problems for linear response.Mark Pollicott, University of Warwick11th Floor Lecture Hall
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10:00 - 10:45On the fractal geometry of horseshoes in arbitrary dimensionsCarlos Gustavo Moreira, IMPA11th Floor Lecture Hall
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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 subsystemsPablo Shmerkin, Torcuato Di Tella University11th Floor Lecture Hall
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12:30 - 1:15Sums of Cantor sets and convolutions of singular measuresAnton Gorodetski, University of California, Irvine11th Floor Lecture Hall
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1:30 - 3:15Break for Lunch / Free Time 11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space