What is he best known for?
The fields of study he is best known for:
- Mathematical analysis
- Geometry
- Algebra
Artur Avila spends much of his time researching Mathematical analysis, Spectrum, Lyapunov exponent, Pure mathematics and Absolute continuity.
The various areas that he examines in his Mathematical analysis study include Translation surface and Rigidity.
His studies in Spectrum integrate themes in fields like Phase transition and Mathematical physics.
His study in Pure mathematics is interdisciplinary in nature, drawing from both Measure and Constant.
His work in Absolute continuity addresses issues such as Discrete mathematics, which are connected to fields such as Stochastic dynamics, Space and Invariant measure.
His Ergodic theory study combines topics in areas such as Dynamical system and Calculus.
His most cited work include:
- The Ten Martini Problem (264 citations)
- Weak mixing for interval exchange transformations and translation flows (163 citations)
- Almost localization and almost reducibility (143 citations)
What are the main themes of his work throughout his whole career to date?
Artur Avila mainly investigates Pure mathematics, Mathematical analysis, Lyapunov exponent, Ergodic theory and Conjecture.
His Pure mathematics research is multidisciplinary, incorporating elements of Mixing and Exponential function.
His work deals with themes such as Novikov self-consistency principle, Invariant measure, Spectrum and Parameter space, which intersect with Mathematical analysis.
His study in the field of Lyapunov equation is also linked to topics like Open set, Spectral radius, Codimension and Dynamical systems theory.
His Ergodic theory research includes themes of Discrete mathematics, Countable set, Quadratic equation, Schrödinger's cat and Ergodicity.
His work carried out in the field of Conjecture brings together such families of science as Structure and Closure.
He most often published in these fields:
- Pure mathematics (70.85%)
- Mathematical analysis (37.69%)
- Lyapunov exponent (29.65%)
What were the highlights of his more recent work (between 2016-2021)?
- Pure mathematics (70.85%)
- Diffeomorphism (9.55%)
- Conjecture (24.12%)
In recent papers he was focusing on the following fields of study:
Artur Avila mostly deals with Pure mathematics, Diffeomorphism, Conjecture, Ergodic theory and Irrational number.
His Pure mathematics research includes elements of Entropy, Fixed point and Mixing.
His work in Diffeomorphism covers topics such as Closed manifold which are related to areas like Geometry and topology and Discrete mathematics.
His research in Conjecture intersects with topics in Structure, Closure and Phase.
Artur Avila merges Ergodic theory with Lyapunov exponent in his study.
His work on Irrational rotation as part of general Irrational number study is frequently linked to Alpha, therefore connecting diverse disciplines of science.
Between 2016 and 2021, his most popular works were:
- Sharp phase transitions for the almost Mathieu operator (51 citations)
- Symplectic and isometric SL(2,#x211D;)-invariant subbundles of the Hodge bundle (19 citations)
- Spectral theory of extended Harper’s model and a question by Erdős and Szekeres (18 citations)
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