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Mathematics

D-Index
41
Citations
5757
World Ranking
1940
National Ranking
33

Research.com Recognitions

  • 2019 - Member of the National Academy of Sciences
  • 2014 - Fields Medal of International Mathematical Union (IMU) For his profound contributions to dynamical systems theory, which have changed the face of the field, using the powerful idea of renormalization as a unifying principle.

Overview

Artur Avila is affiliated with the University of Zurich in Switzerland. Their research spans several areas within mathematics and physics, with a focus on mathematical physics and dynamical systems.

The main fields of study represented in their work include:

  • Mathematics
  • Physics and Astronomy

Within these fields, Avila's research contributions cover subfields such as:

  • Mathematical Physics
  • Statistical and Nonlinear Physics
  • Geometry and Topology
  • Applied Mathematics
  • Computational Theory and Mathematics

The topics most frequently addressed in their publications are:

  • Quantum chaos and dynamical systems
  • Spectral Theory in Mathematical Physics
  • Mathematical Dynamics and Fractals
  • Advanced Mathematical Modeling in Engineering
  • Numerical methods in inverse problems
  • Holomorphic and Operator Theory
  • Geometric and Algebraic Topology

Avila's published papers have appeared in a variety of venues, including:

  • arXiv (Cornell University)
  • Geometric and Functional Analysis
  • Astérisque
  • Duke Mathematical Journal
  • Annals of Mathematics

Recent notable papers include:

  • "Lebesgue measure of Feigenbaum Julia sets" (2022) in Annals of Mathematics
  • "On the abominable properties of the almost Mathieu operator with well-approximated frequencies" (2024) in Duke Mathematical Journal
  • "Schrödinger operators with potentials generated by hyperbolic transformations: I-positivity of the Lyapunov exponent" (2022) in Inventiones mathematicae
  • "Quantitative weak mixing for interval exchange transformations" (2023) in Geometric and Functional Analysis
  • "Mixing for smooth time-changes of general nilflows" (2021) in Advances in Mathematics

Frequent co-authors with whom Avila has collaborated include:

  • David Damanik
  • Zhenghe Zhang
  • Giovanni Forni
  • Yoram Last
  • Mira Shamis

Avila has received recognition in their field, notably being awarded the Fields Medal by the International Mathematical Union in 2014, cited for contributions to dynamical systems theory through the use of renormalization as a unifying principle.

Additionally, Avila was elected as a Member of the National Academy of Sciences in 2019.

Best Publications

  • The Ten Martini Problem

    Artur Avila;Svetlanaya Jitomirskaya

  • Weak mixing for interval exchange transformations and translation flows

    Artur Avila;Giovanni Forni

  • Reducibility or nonuniform hyperbolicity for quasiperiodic Schrodinger cocycles

    Artur Ávila;Raphaël Krikorian

  • Global theory of one-frequency Schrödinger operators

    Artur Avila;Artur Avila

  • Exponential mixing for the Teichmüller flow

    Artur Avila;Sébastien Gouëzel;Jean-Christophe Yoccoz

  • Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture

    Artur Avila;Marcelo Viana

  • Almost localization and almost reducibility

    Artur Avila;Svetlanaya Jitomirskaya

  • Extremal Lyapunov exponents: an invariance principle and applications

    Artur Avila;Artur Avila;Marcelo Viana

  • Sharp phase transitions for the almost Mathieu operator

    Artur Avila;Jiangong You;Qi Zhou

  • A KAM SCHEME FOR SL(2, R) COCYCLES WITH LIOUVILLEAN FREQUENCIES

    Artur Avila;Bassam Fayad;Raphaël Krikorian

  • Regular or stochastic dynamics in real analytic families of unimodal maps

    Artur Avila;Mikhail Lyubich;Mikhail Lyubich;Welington de Melo

  • Almost reducibility and absolute continuity I

    Artur Avila

  • On the regularization of conservative maps

    Artur Avila;Artur Avila

  • The absolutely continuous spectrum of the almost Mathieu operator

    Artur Avila

  • Statistical properties of unimodal maps: the quadratic family

    Artur Ávila;Carlos Gustavo Moreira

  • Absolute continuity, Lyapunov exponents and rigidity I: geodesic flows

    Artur Avila;Marcelo Viana;Amie Wilkinson

  • Absolute continuity of the integrated density of states for the almost Mathieu operator with non-critical coupling

    Artur Avila;David Damanik

  • On the Spectrum and Lyapunov Exponent of Limit Periodic Schrödinger Operators

    Artur Avila;Artur Avila

  • An integrable deformation of an ellipse of small eccentricity is an ellipse

    Artur Avila;Jacopo De Simoi;Vadim Kaloshin

  • Complex one-frequency cocycles

    Artur Avila;Svetlana Jitomirskaya;Christian Sadel

  • Spectral theory of extended Harper’s model and a question by Erdős and Szekeres

    A. Avila;S. Jitomirskaya;C. A. Marx

Frequent Co-Authors

Svetlana Jitomirskaya
Svetlana Jitomirskaya University of California, Irvine
David Damanik
David Damanik Rice University
Marcelo Viana
Marcelo Viana Instituto Nacional de Matemática Pura e Aplicada
Barry Simon
Barry Simon California Institute of Technology
Alex Eskin
Alex Eskin University of Chicago
Eduard Looijenga
Eduard Looijenga Utrecht University
Fritz Grunewald
Fritz Grunewald Heinrich Heine University Düsseldorf
John Coates
John Coates University of Cambridge

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