Reading group on Topics in Entropy Zero Dynamics

Future talks

Unless otherwise stated, talks on Fridays at 10.15 in H25.

• 02/05/25   Jonguk Yang and Noam Szyfer,   Cross-ratios and basic tools for 1D dynamics
  

• 09/05/25   Guest talk: Nicole Müller,   Teichmüller Curves
  

• 16/05/25   Jonguk Yang,   Renormalisation for unimodal maps I
  

• 23/05/25   Jonguk Yang,   Renormalisation for unimodal maps II
  

Past talks

Spring 2025

• 11/04/25   Corinna Ulcigrai,   Renormalisation of GIETs II
  Reference: Selim Ghazouani and Corinna Ulcigrai, A priori bounds for GIETs, affine shadows and rigidity of foliations in genus two

• 04/04/25   Corinna Ulcigrai,   Renormalisation of GIETs I
  Reference: Selim Ghazouani and Corinna Ulcigrai, A priori bounds for GIETs, affine shadows and rigidity of foliations in genus two

• 28/03/25   Hao Wu,   Local limit theorems
  Reference: Dmitry Dolgopyat and Omri Sarig, Local Limit Theorems for Inhomogeneous Markov Chains

• 21/03/25   Mihajlo Cekić,   Spectral gap for Anosov flows II
  

• 14/03/25   Mihajlo Cekić,   Spectral gap for Anosov flows I
  

• 07/03/25   Pouya Honaryar,   Measured laminations
  

Autumn 2024

• 12/11/24   Corinna Ulcigrai,   Veech Surfaces III: Veech continued fractions
  

• 28/11/24   Guest talk: Dmitry Dolgopyat,   Local Limit Theorems for non stationary subshifts of finite type
  

• 21/11/24   Corinna Ulcigrai,   Veech Surfaces II
  

• 14/11/24   Corinna Ulcigrai,   Veech Surfaces I
  

• 07/11/24   Guest talk: Hamid Al-Saqban  
  

• 31/10/24  Daniele Galli and Yuriy Tumarkin,   Horocycle flows on abelian covers of surfaces of negative curvature Talk 2
  Reference: Roberto Castorrini and Davide Ravotti, Horocycle flows on abelian covers of surfaces of negative curvature

• 24/10/24   Katy Loyd   Strong sweeping out property
  

• 17/10/24   Daniele Galli and Yuriy Tumarkin,   Horocycle flows on abelian covers of surfaces of negative curvature Talk 1
  Reference: Roberto Castorrini and Davide Ravotti, Horocycle flows on abelian covers of surfaces of negative curvature

• 08/10/24   Adam Kanigowski,   Higher order mixing for mixing dynamical systems, Talk 2
  

• 03/10/24   Adam Kanigowski,   Higher order mixing for mixing dynamical systems, Talk 1
  

Spring 2024

• 06/06/24   Przemysłav Berk and Frank Trujillo,  Ergodicity of skew-products over typical IETs
  Reference: F. Argentieri, P. Berk, F. Trujillo, Ergodicity of skew-products over typical IETs
• 30/05/24   Guest talk: Magali Jay,  Tiling billiards and IETs
  References:
  • P. Baird-Smith, D. Davis, E. Fromm, S. Iyer, Tiling billards on triangle tilings, and interval exchange transformations
  • Pascal Hubert and Olga Paris-Romaskevich, Triangle Tiling Billiards and the Exceptional Family of their Escaping Trajectories: Circumcenters and Rauzy Gasket
  • Olga Paris-Romaskevich, Trees and flowers on a billiard table
• 02/05/24   Guest talk: Irene Pasquinelli,  Mapping class group orbit closures for non-orientable surfaces 2
  Reference: V. Erlandsson, M. Gendulphe, I. Pasquinelli and J. Souto, Mapping class group orbit closures for non-orientable surfaces
• 25/04/24   Guest talk: Irene Pasquinelli,  Mapping class group orbit closures for non-orientable surfaces 1
  Reference: V. Erlandsson, M. Gendulphe, I. Pasquinelli and J. Souto, Mapping class group orbit closures for non-orientable surfaces
• 18/04/24   Sophie Schmidhuber,  Limit Sets of Non-orientable Mapping Class Groups II
  Reference: Sayantan Khan, The limit set of non-orientable mapping class groups
• 11/04/24   Sophie Schmidhuber,  Limit Sets of Non-orientable Mapping Class Groups I
  Reference: Sayantan Khan, The limit set of non-orientable mapping class groups
• 26/03/24   Chris Lutsko,  Perfect Retroreflectors and Billiard Dynamics
  Reference: P. Bachurin, K. Khanin, J. Marklof and A. Plakhov, Perfect retroreflectors and billiard dynamics
• 21/03/24   Pouya Honaryar,  Introduction to Teichmüller Space of Hyperbolic Structures
  Reference: Benson Farb and Dan Margalit, A Primer on Mapping Class Groups
• 19/03/24   Yuriy Tumarkin,  Cohomological Methods 2: Kontsevich-Zorich Cocycle
  Reference: Giovanni Forni, Effective Unique Ergodicity and Weak Mixing of Translation Flows
• 14/03/24   Przemysłav Berk,   Ergodic Decomposition in Infinite Ergodic Theory
  Reference: Jon Aaronson, An Introduction to Infinite Ergodic Theory, volume 50 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 1997.

Autumn 2023

• 28/11/23   Sophie Schmidhuber,   Geodesic and Horocycle Flows 3: Patterson-Sullivan Measure
  Reference: Barbara Schapira, Dynamics of Geodesic and Horocyclic Flows
• 07/11/23   Yuriy Tumarkin,  Cohomological Methods 1: Number of ergodic measures
  Reference: Giovanni Forni, Effective Unique Ergodicity and Weak Mixing of Translation Flows
• 25/10/23   Sophie Schmidhuber and Yuriy Tumarkin,   Geodesic and Horocycle Flows 2: Ergodicity and Mixing
  Reference: Barbara Schapira, Dynamics of Geodesic and Horocyclic Flows
• 03/10/23   Sophie Schmidhuber,   Geodesic and Horocycle Flows 1: Topological Dynamics
  Reference: Barbara Schapira, Dynamics of Geodesic and Horocyclic Flows

Spring 2023

• 12/05/23   Frank Trujillo,   Hausdorff dimension of invariant measures of piecewise smooth circle homeomorphisms
  Reference: Frank Trujillo, On the Hausdorff dimension of invariant measures of piecewise smooth circle homeomorphisms
• 31/03/24   Yuriy Tumarkin,  Bratteli Diagrams and Vershik Maps for IETs
  References:
  • Alexander Bufetov, Limit theorems for suspension flows over Vershik automorphisms
  • Kathryn Lindsey and Rodrigo Treviño, Infinite type flat surface models of ergodic systems
• 24/03/23   Corinna Ulcigrai,   Regularity of Conjugacies Between GIETs and IETs
  Reference: Selim Ghazouani and Corinna Ulcigrai, Regularity of conjugacies of linearizable generalized interval exchange transformations
• 17/03/23   Andrea Ulliana,   Invariant Manifolds for Hyperbolic Diffeomorphisms 2: Regularity of Invariant Submanifolds
  Reference: Michael Schub, Global Stability of Dynalmical Systems
• 10/03/23   Andrea Ulliana,   Invariant Manifolds for Hyperbolic Diffeomorphisms 1: Existence of Stable and Unstable Manifolds
  Reference: Michael Schub, Global Stability of Dynalmical Systems
• 03/03/23   Guest talk: Stefano Marmi,   Brjuno Functions
  Reference: S. Marmi, P. Moussa, and J.-C. Yoccoz, Some properties of real and complex Brjuno functions, In Frontiers in Number Theory, Physics, and Geometry. I, pp. 601–623. Springer, Berlin, 2006

Autumn 2022

• 16/12/22   Hao Wu,   Recurrence and Ergodicity of Random Walks Driven by Rotations
  Reference: Dmitry Dolgopyat and Bassam Fayad, Limit theorems for toral translations
• 09/12/22   Yuriy Tumarkin,  Maharam Measures
  Reference: J. Aaronson, H. Nakada, O. Sarig and R. Solomyak, Invariant measures and asymptotics for some skew products
• 25/11/22   Yuriy Tumarkin,  The Infinite Staircase
  References:
  • P. Hooper, P. Hubert and B. Weiss, Dynamics on the inifinite staircase
  • J. Aaronson, H. Nakada, O. Sarig and R. Solomyak, Invariant measures and asymptotics for some skew products
• 18/11/22   Frank Trujillo,   Dynamical Partitions for Multicritical Circle Maps
  Reference: Edson de Faria and Pablo Guarino, Dynamics of multicritical circle maps
• 04/11/22   Corinna Ulcigrai,   Deviations of Ergodic Averages for IETs
  Reference: Anton Zorich, Deviation for interval exchange transformations
• 28/10/22   Guido Marinoni,   Introduction to Rauzy-Veech Induction
  Reference: Vincent Delecroix, Interval Exchange Transformations
• 20/10/22   Jonguk Yang,   Koebe Distortion
  Reference:
• 07/10/22   Jonguk Yang,   A Priori Bounds for Critical Circle Maps
  Reference: Edson de Faria and Welington de Melo, Rigidity of critical circle mappings I