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Description

An ICTP Meeting

The meeting belongs to a series of conferences organized since 2001 (Bedlewo, Poland (2023 and 2013), Luminy, France (2019 and 2011) Provo, USA (2017), Olmué, Chile (2015), Beijing, China (2009), Chicago, IL, USA (2006), Búzios, Brazil (2003), Evanston, USA (2001)). They have been instrumental for collaborations among the participants, furthering the subject and leading to new connections between different directions in the field.

Topics:
Partial hyperbolicity, Nonuniform hyperbolicity, Lyapunov exponents | Bifurcations: homoclinic tangencies, heterodimensional cycles | Typical phenomena: robustness, genericity, prevalence | Physical and Sinai-Ruelle-Bowen measures | Dimension theory, Thermodynamical Formalism | Statistical properties: decay of correlations, limit theorems | Symbolic dynamics, entropy, coding | Classification of dynamical systems, group actions and rigidity phenomena.
  • Thermodynamic formalism in holomorphic dynamics: Fabrizio BIANCHI (Università di Pisa, Italy) and Mary Yan HE (University of Oklahoma, USA)
  • Random walks on projective spaces: Jialun LI (Ecole Polytechnique, France) and Wenyu PAN (University of Toronto, Canada)
  • Rigidity of abelian actions: Kurt VINHAGE (University of Utah, USA)

The related Beyond Uniform Hyperbolicity II: Unstable entropy, generalized u-Gibbs measures and classification complexity (smr 4157) will take place the week after, from 9 to 13 June 2025.
Applications need to be made separately here: https://indico.ictp.it/event/10935/

Participants selected for both will receive a joint invitation letter.

Grants: A limited number of grants are available to support the attendance of selected participants, with priority given to participants from developing countries. There is no registration fee.

Material

Beyond Uniform Hyperbolicity I: Higher rank actions, random walks and holomorphic dynamics | (smr 4076)
Go to day
  • Monday, 2 June 2025
    • 08:30 - 09:00
      • 08:30 Registration 30' 
        Upon arrival, Visitors not staying in the ICTP Guest Houses, are kindly requested to complete registration formalities at the Leonardo Building (Lobby) from 08.30 to 09.00.
    • 09:00 - 17:10
      • 09:00 Opening Remarks 20'
        Speaker: Jairo DA SILVA BOCHI (Penn State University, USA), Danijela DAMJANOVIC (Kungliga Tekniska Högskolan, Sweden), Katrin GELFERT (Institute of Mathematics, Federal University of Rio de Janeiro, Brazil), Andrey GOGOLEV (Ohio State University, USA), Andy HAMMERLINDL (Monash University, Australia) Alejandro KOCSARD (Federal Fluminense University, Brazil), Michele TRIESTINO (Bourgogne University, France), Disheng XU (Great Bay University School of Science, China), Stefano LUZZATTO (ICTP, Italy)
        Material: Video
      • 09:20 Minimality of strong foliations of Anosov diffeomorphisms 1h0'
        Speaker: Amie WILKINSON (University of Chicago, USA)
        Material: Abstract Video
      • 10:20 Coffee Break 40'
      • 11:00 Thermodynamic formalism in holomorphic dynamics - Part I 1h0'
        Speaker: Fabrizio BIANCHI (Università di Pisa, Italy) and Mary Yan HE (University of Oklahoma, USA)
        Material: Video
      • 12:00 Introduction and statement of the main results 1h0'
        Speaker: Wenyu PAN (University of Toronto, Canada)
        Material: Video
      • 13:00 Lunch Break 2h20'
      • 15:20 Fundamentals of (partially) hyperbolic abelian group actions 50'
        Speaker: Kurt VINHAGE (University of Utah, USA)
        Material: Video
      • 16:20 Absolute continuity of stationary measures 50'
        Speaker: Davi Joel DOS ANJOS OBATA (Brigham Young University, USA)
        Material: Video
    • 17:20 - 18:10 Lightning talks
      • 17:20 Strong Positive Recurrence and Exponential Mixing for Interval Maps 10'
        Speaker: Hengyi LI (Paris-Saclay University, France)
      • 17:30 The cohomological equation over parabolic base 10'
        Speaker: Spencer DURHAM (USA)
      • 17:40 Quadratic growth for the derivatives of iterates of interval diffeomorphisms 10'
        Speaker: Leonardo Andres DINAMARCA OPAZO (Santiago de Chile University, Chile)
      • 17:50 Invariant sets for homeomorphisms of hyperbolic 3-manifolds 10'
        Speaker: Elena Isabel GOMES PEREIRA (Paris-Saclay University, France)
      • 18:00 Measures of maximal entropy of smooth saddle surface endomorphisms 10'
        Speaker: Matteo GHEZAL (Paris-Saclay University, France)
  • Tuesday, 3 June 2025
    • 09:00 - 18:10
      • 09:00 Entropy growth argument for Bernoulli convolution based on 1h0'
        Speaker: Jialun LI (Ecole Polytechnique, France)
        Material: Video
      • 10:00 Break / Posters 40'
      • 10:40 Thermodynamic formalism in holomorphic dynamics - Part II 1h0'
        Speaker: Fabrizio BIANCHI (Università di Pisa, Italy) and Mary Yan HE (University of Oklahoma, USA)
        Material: Video
      • 11:50 Solenoidal surfaces of finite type and their horocycle flows 50'
        Speaker: Matilde MARTÍNEZ GARCIA (Institute of Mathematics and Statistics, Uruguay)
        Material: Video
      • 13:00 Lunch Break 2h20'
      • 15:20 Expanding on Average Random Dynamics 50'
        Speaker: Jonathan DEWITT (University of Maryland, USA)
        Material: Video
      • 16:20 Diophantine Approximation on the Kleinian Circle Packing 50' ( Euler-Lagrange seminar room )
        Speaker: Kangrae PARK (Seoul National University, Korea)
      • 16:20 Invariant distributions of partially hyperbolic systems: fractal graphs, excessive regularity, and rigidity 50' ( Budinich Lecture Hall )
        Speaker: Jiesong ZHANG (Peking University, China)
      • 17:20 Quasi-conformal behaviours in linear cocycles 50' ( Euler-Lagrange seminar room )
        Speaker: Zahra RESHADAT (IPM School of Mathematics, Iran)
      • 17:20 Centralizer rigidity of partially hyperbolic diffeomorphisms 50' ( Budinich Lecture Hall )
        Speaker: Sven SANDFELDT (Royal Institute of Technology, Sweden)
    • 19:00 - 21:00
      • 19:00 Welcome Reception 2h0' ( Adriatico Guest House Terrace ) 
        All Participants are cordially invited to the Welcome Reception
  • Wednesday, 4 June 2025
    • 09:00 - 17:00
      • 09:00 Tools for rigidity 1h0'
        Speaker: Kurt VINHAGE (University of Utah, USA)
        Material: Video
      • 10:00 Break 40'
      • 10:40 Non-concentration of stationary measures on arithmetic sequence via Fourier decay 1h0'
        Speaker: Jialun LI (Ecole Polytechnique, France)
        Material: Video
      • 11:50 Unicritical Surface Maps and Their Renormalizations 50'
        Speaker: Sylvain Felix CROVISIER (University Paris-Saclay)
        Material: Abstract Video
      • 12:40 Lunch Break 2h0'
      • 14:40 Free afternoon 2h20'
  • Thursday, 5 June 2025
    • 09:00 - 18:10
      • 09:00 Variational principle for Anosov representations; proof of the dimension formula of limit sets 1h0'
        Speaker: Wenyu PAN (University of Toronto, Canada)
        Material: Video
      • 10:00 Group Photo 5'
      • 10:05 Break/Posters 35'
      • 10:40 Thermodynamic formalism in holomorphic dynamics - Part III 1h0'
        Speaker: Fabrizio BIANCHI (Università di Pisa, Italy) and Mary Yan HE (University of Oklahoma, USA)
        Material: Video
      • 11:50 Blenders and Ergodicity 50'
        Speaker: Meysam NASSIRI (Institute for Research in Fundamental Sciences, Iran)
        Material: Video
      • 13:00 Lunch Break 2h20'
      • 15:20 Hyperbolicity of renormalization of quasi-periodic cocycles 50'
        Speaker: Yi PAN (nstitute of Science and Technology, Austria)
        Material: Video
      • 16:20 Geometry of the Hyperbolic Locus in SL(2,R)^3 50' ( Euler-Lagrange seminar room )
        Speaker: William WOOD (University of Califormia, Riverside, USA)
      • 16:20 On the original Ulam's problem and its quantization 50' ( Leonardo Building - Budinich Lecture Hall )
        Speaker: Jing ZHOU (Great Bay University School of Sciences, China)
      • 17:20 Exponentially mixing SRB measures are Bernoulli 50' ( Euler-Lagrange seminar room )
        Speaker: Amadeus CABRAL MALDONADO (Northwestern University, USA)
      • 17:20 Partially Hyperbolic Diffeomorphisms With a Finite Number of Measures of Maximal Entropy 50' ( Leonardo Building - Budinich Lecture Hall )
        Speaker: Juan Carlos MONGEZ DURAN (Federal University of Ceará, Brazil)
  • Friday, 6 June 2025
    • 09:00 - 17:10
      • 09:00 Thermodynamic formalism in holomorphic dynamics - Part IV 1h0'
        Speaker: Fabrizio BIANCHI (Università di Pisa, Italy) and Mary Yan HE (University of Oklahoma, USA)
        Material: Video
      • 10:00 Break 40'
      • 10:40 Non-rigidity and partial rigidity 1h0'
        Speaker: Kurt VINHAGE (University of Utah, USA)
        Material: Video
      • 11:50 Adelic loop spaces 50'
        Speaker: Alberto VERJOVSKY SOLA (National Autonomous University of Mexico, Mexico)
        Material: Video
      • 13:00 Lunch Break 2h20'
      • 15:20 Full flexibility of entropies among ergodic measures for partially hyperbolic diffeomorphisms 50'
        Speaker: Lorenzo DIAZ (Pontifical Catholic University of Rio de Janeiro, Brazil)
        Material: Video
      • 16:20 Linear response for discontinuous perturbations of smooth endomorphisms 50'
        Speaker: Giovanni CANESTRARI (Bologna University, Italy)
      • 16:20 Unstable minimal sets for collapsed Anosov flows 50' ( Leonardo Building - Budinich Lecture Hall )
        Speaker: Santiago MARTINCHICH RODRIGUEZ (University of the Republic, Uruguay)
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