Artur Avila Cordeiro de Melo

Bolsista de Produtividade em Pesquisa do CNPq - Nível 1A

  • Endereço para acessar este CV: http://lattes.cnpq.br/8907835195811403
  • Última atualização do currículo em 25/04/2017


Possui graduação em Matemática pela Universidade Federal do Rio de Janeiro (2001), mestrado em Matemática pela Associação Instituto Nacional de Matemática Pura e Aplicada (1997) e doutorado em Matemática pela Associação Instituto Nacional de Matemática Pura e Aplicada (2001). Atualmente é pesquisador da Associação Instituto Nacional de Matemática Pura e Aplicada e pesquisador - Centre National de la Recherche Scientifique. Tem experiência na área de Matemática, com ênfase em Sistemas Dinâmicos (Texto informado pelo autor)


Identificação


Nome
Artur Avila Cordeiro de Melo
Nome em citações bibliográficas
AVILA, A.;AVILA, ARTUR

Endereço


Endereço Profissional
Instituto Nacional de Matemática Pura e Aplicada.
Estrada Dona Castorina, 110
Horto
22460-320 - Rio de Janeiro, RJ - Brasil
Telefone: (21) 25295000
URL da Homepage: http://www.proba.jussieu.fr/pageperso/artur


Formação acadêmica/titulação


1998 - 2001
Doutorado em Matemática.
Instituto Nacional de Matemática Pura e Aplicada, IMPA, Brasil.
Título: Bifurcações de tranformações unimodais sob os pontos de vistas topológico e métrico, Ano de obtenção: 2001.
Orientador: Welington Celso de Melo.
Bolsista do(a): Conselho Nacional de Desenvolvimento Científico e Tecnológico, CNPq, Brasil.
1996 - 1997
Mestrado em Matemática.
Instituto Nacional de Matemática Pura e Aplicada, IMPA, Brasil.
Título: Não divulgada,Ano de Obtenção: 2001.
Orientador: Elon lages Lima.
Bolsista do(a): Conselho Nacional de Desenvolvimento Científico e Tecnológico, CNPq, Brasil.
1997 - 2001
Graduação em Matemática.
Universidade Federal do Rio de Janeiro, UFRJ, Brasil.
Título: não divulgada.
Orientador: não divulgada.




Atuação Profissional



Clay Institute, CLAY, Estados Unidos.
Vínculo institucional

2006 - 2009
Vínculo: Bolsista, Enquadramento Funcional: Pesquisador


Instituto Nacional de Matemática Pura e Aplicada, IMPA, Brasil.
Vínculo institucional

2006 - Atual
Vínculo: Professor Visitante, Enquadramento Funcional: Pesquisador


Centre National de la Recherche Scientifique, CNRS, França.
Vínculo institucional

2003 - Atual
Vínculo: Funcionario, Enquadramento Funcional: Pesquisador


College de France, COLLEGE FRANCE, França.
Vínculo institucional

2001 - 2003
Vínculo: Pos Doutorado, Enquadramento Funcional: Pesquisador



Membro de corpo editorial


2010 - Atual
Periódico: Publications Mathématiques (Bures-sur-Yvette)


Áreas de atuação


1.
Grande área: Ciências Exatas e da Terra / Área: Matemática / Subárea: Geometria e Topologia/Especialidade: Sistemas Dinâmicos.


Idiomas


Francês
Compreende Razoavelmente, Fala Razoavelmente, Lê Razoavelmente, Escreve Razoavelmente.
Inglês
Compreende Razoavelmente, Fala Razoavelmente, Lê Razoavelmente, Escreve Razoavelmente.


Prêmios e títulos


2015
TWAS-Lenovo Science Prize, TWAS.
2014
Medalha Fields, IMU.
2013
Premio da SBM, SBM.
2013
Twas Prize, Twas.
2012
Early Career Award, IAMP.
2011
Michael Brin Prize, .
2009
Grand Prix Jacques Herbrand, Academie des Sciences.
2008
Wolff Memorial Lectures, Caltech.
2008
Prize of the European Mathematical Society, European Mathematical Society.
2006
Medalha de Bronze, CNRS.
2006
Premio Salem, .
2005
Curso Peccot, College de France.
1995
Medalha de Ouro, Olimpiada Internacional de Matematica.


Produções



Produção bibliográfica
Artigos completos publicados em periódicos

1.
AVILA, ARTUR2016AVILA, ARTUR; DE SIMOI, JACOPO ; KALOSHIN, VADIM . An integrable deformation of an ellipse of small eccentricity is an ellipse. Annals of Mathematics, v. 184, p. 527-558, 2016.

2.
AVILA, ARTUR2016AVILA, ARTUR; DELECROIX, VINCENT . Weak mixing directions in non-arithmetic Veech surfaces. Journal of the American Mathematical Society, v. 29, p. 1167-1208, 2016.

3.
AVILA, ARTUR2016AVILA, ARTUR; CANDELA, PABLO . Towers for commuting endomorphisms, and combinatorial applicationsTours pour endomorphismes commutants, et applications combinatoires. Annales de l'Institut Fourier, v. 66, p. 1529-1544, 2016.

4.
AVILA, ARTUR2016AVILA, ARTUR; HUBERT, PASCAL ; SKRIPCHENKO, ALEXANDRA . On the Hausdorff dimension of the Rauzy gasket. BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE, v. 144, p. 539-568, 2016.

5.
AVILA, ARTUR2016AVILA, ARTUR; HUBERT, PASCAL ; SKRIPCHENKO, ALEXANDRA . Diffusion for chaotic plane sections of 3-periodic surfaces. INVENTIONES MATHEMATICAE, v. 206, p. 109-146, 2016.

6.
AVILA, A.2016AVILA, A.; CROVISIER, S. ; WILKINSON, A. . Diffeomorphisms with positive metric entropy. Publications Mathematiques de l IHES, v. 124, p. 319-347, 2016.

7.
AVILA, A.2015AVILA, A.; FAYAD, B. ; KOCSARD, A. . On manifolds supporting distributionally uniquely ergodic diffeomorphisms. Journal of Differential Geometry, v. 99, p. 191-213, 2015.

8.
AVILA, ARTUR2015AVILA, ARTUR. On the Kotani-Last and Schrödinger conjectures. Journal of the American Mathematical Society, v. 28, p. 579-616, 2015.

9.
AVILA, ARTUR2015AVILA, ARTUR; KRIKORIAN, RAPHAËL . Monotonic cocycles. Inventiones Mathematicae, v. 202, p. 271-331, 2015.

10.
AVILA, ARTUR2015AVILA, ARTUR. Global theory of one-frequency Schrödinger operators. Acta Mathematica, v. 215, p. 1-54, 2015.

11.
AVILA, ARTUR2015AVILA, ARTUR; VIANA, MARCELO ; WILKINSON, AMIE . Absolute continuity, Lyapunov exponents and rigidity I: geodesic flows. Journal of the European Mathematical Society (Print), v. 17, p. 1435-1462, 2015.

12.
AVILA, A.2015AVILA, A.; DOLGOPYAT, D. ; DURYEV, E. ; SARIG, O. . The visits to zero of a random walk driven by an irrational rotation. Israel Journal of Mathematics, v. 207, p. 653-717, 2015.

13.
AVILA, ARTUR2014AVILA, ARTUR; DAMANIK, DAVID ; ZHANG, ZHENGHE . Singular Density of States Measure for Subshift and Quasi-Periodic Schrödinger Operators. Communications in Mathematical Physics, v. 330, p. 469-498, 2014.

14.
AVILA, ARTUR2014AVILA, ARTUR; JITOMIRSKAYA, SVETLANA ; SADEL, CHRISTIAN . Complex one-frequency cocycles. Journal of the European Mathematical Society (Print), v. 16, p. 1915-1935, 2014.

15.
AVILA, ARTUR2013AVILA, ARTUR; GOUËZEL, SÉBASTIEN . Small eigenvalues of the Laplacian for algebraic measures in moduli space, and mixing properties of the Teichmüller flow. Annals of Mathematics, v. 178, p. 385-442, 2013.

16.
AVILA, ARTUR2013AVILA, ARTUR; MATHEUS, CARLOS ; YOCCOZ, JEAN-CHRISTOPHE . $${SL(2, mathbb{R})}$$ S L ( 2 , R ) -invariant probability measures on the moduli spaces of translation surfaces are regular. Geometric and Functional Analysis (Printed ed.), v. 23, p. 1705-1729, 2013.

17.
AVILA, A.;AVILA, ARTUR2013AVILA, A.; SANTAMARIA, J. ; VIANA, M. . Holonomy invariance: rough regularity and applications to Lyapunov exponents. Astérisque, v. 358, p. 13-74, 2013.

18.
AVILA, ARTUR2013AVILA, ARTUR. On rigidity of critical circle maps. Sociedade Brasileira de Matematica. Boletim, Nova Serie, v. 44, p. 611-619, 2013.

19.
AVILA, A.;AVILA, ARTUR2012AVILA, A.; BOCHI, J. . Nonuniform hyperbolicity, global dominated splittings and generic properties of volume-preserving diffeomorphisms. Transactions of the American Mathematical Society, v. 364, p. 2883-2907, 2012.

20.
AVILA, A.;AVILA, ARTUR2012AVILA, A.; BOCHI, J. ; DAMANIK, D. . Opening gaps in the spectrum of strictly ergodic Schrodinger operators. Journal of the European Mathematical Society (Print), v. 14, p. 61-106, 2012.

21.
AVILA, ARTUR2012AVILA, ARTUR; RESENDE, MARIA JOÃO . Exponential Mixing for the Teichmuller flow in the Space of Quadratic Differentials. Commentarii Mathematici Helvetici (Printed ed.), v. 87, p. 589-638, 2012.

22.
AVILA, A.;AVILA, ARTUR2011AVILA, A.; LYUBICH, M. ; SHEN, W. . Parapuzzle of the Multibrot set and typical dynamics of unimodal maps. Journal of the European Mathematical Society (Print), v. 13, p. 27-56, 2011.

23.
AVILA, A.;AVILA, ARTUR2011AVILA, A.; JITOMIRSKAYA, J. . Hölder continuity of absolutely continuous spectral measures for one-frequency Schrödinger operators. Communications in Mathematical Physics, v. 301, p. 563-581, 2011.

24.
AVILA, A.;AVILA, ARTUR2011AVILA, A.. Density of positive Lyapunov exponents for SL(2,R) cocycles. Journal of the American Mathematical Society, v. 24, p. 999-1014, 2011.

25.
AVILA, A.;AVILA, ARTUR2011AVILA, A.; FAYAD, B. ; KRIKORIAN, R. . A KAM scheme for SL(2,R) cocycles with Liouvillean frequencies. Geometric and Functional Analysis (Printed ed.), v. 21, p. 1001-1019, 2011.

26.
AVILA, A.;AVILA, ARTUR2011AVILA, A.; Lyubich, M. . The full renormalization horseshoe for unimodal maps of higher degree: exponential contraction along hybrid classes. Publications Mathématiques (Bures-sur-Yvette), v. 114, p. 171-223, 2011.

27.
AVILA, A.2011AVILA, A.; FORNI, G. ; ULCIGRAI, C. . Mixing for time-changes of Heisenberg nilflows. Journal of Differential Geometry, v. 89, p. 369-410, 2011.

28.
AVILA, A.;AVILA, ARTUR2011AVILA, A.; KOCSARD, A. . Cohomological equations and invariant distributions for minimal circle diffeomorphisms. Duke Mathematical Journal, v. 158, p. 501-536, 2011.

29.
AVILA, A.;AVILA, ARTUR2010AVILA, A.; JITOMIRSKAYA, J. . Almost localization and almost reducibility. Journal of the European Mathematical Society (Print), v. 12, p. 93-131, 2010.

30.
AVILA, A.;AVILA, ARTUR2010AVILA, A.; BOCHI, J. ; Yoccoz, J.-C. . Uniformly hyperbolic finite-valued SL(2,R)-cocycles. Commentarii Mathematici Helvetici (Printed ed.), v. 85, p. 813-884, 2010.

31.
AVILA, A.;AVILA, ARTUR2010AVILA, A.. On the regularization of conservative maps. Acta Mathematica, v. 205, p. 5-18, 2010.

32.
AVILA, A.;AVILA, ARTUR2010AVILA, A.; VIANA, M. . Extremal Lyapunov exponents: an invariant principle and applications. Inventiones Mathematicae, v. 181, p. 115-174, 2010.

33.
AVILA, ARTUR2010AVILA, ARTUR; LAST, YORAM ; SIMON, BARRY . Bulk universality and clock spacing of zeros for ergodic Jacobi matrices with absolutely continuous spectrum. ANAL PDE, v. 3, p. 81-108, 2010.

34.
AVILA, A.;AVILA, ARTUR2009 AVILA, A.; JITOMIRSKAYA, J. . The Ten Martini Problem. Annals of Mathematics, v. 170, p. 303-342, 2009.

35.
AVILA, A.;AVILA, ARTUR2009AVILA, A.; KAHN, J. ; LYUBICH, M. ; SHEN, W. . Combinatorial rigidity for unicritical polynomials. Annals of Mathematics, v. 170, p. 783-797, 2009.

36.
AVILA, A.;AVILA, ARTUR2009AVILA, A.; BOCHI, J. ; DAMANIK, D. . Cantor Spectrum for Schrödinger Operators with Potentials arising from Generalized Skew-shifts. Duke Mathematical Journal, v. 146, p. 253-280, 2009.

37.
AVILA, A.;AVILA, ARTUR2009AVILA, A.. On the spectrum and Lyapunov exponent of limit periodic Schrodinger operators. Communications in Mathematical Physics, v. 288, p. 907-918, 2009.

38.
AVILA, A.;AVILA, ARTUR2009AVILA, A.; BOCHI, J. ; WILKINSON, A. . Nonuniform center bunching and the genericity of ergodicity among C^1 partially hyperbolic symplectomorphisms. Annales Scientifiques de l'Ecole Normale Supérieure, v. 42, p. 931-979, 2009.

39.
AVILA, A.;AVILA, ARTUR2008AVILA, A.; LYUBICH, M. . Hausdorff dimension and conformal measures of Feigenbaum Julia sets. Journal of the American Mathematical Society, v. 21, p. 305-363, 2008.

40.
AVILA, A.;AVILA, ARTUR2008AVILA, A.; DAMANIK, D. . Absolute continuity of the integrated density of states for the almost Mathieu operator with non-critical coupling. Inventiones Mathematicae, v. 172, p. 439-453, 2008.

41.
AVILA, A.;AVILA, ARTUR2007 AVILA, A.; FORNI, G. . Weak mixing for interval exchange transformations and translation flows. Annals of Mathematics, v. 175, p. 635-664, 2007.

42.
AVILA, A.;AVILA, ARTUR2007AVILA, A.; VIANA, M. . Simplicity of Lyapunov spectra: proof of the Zorich-Kontsevich conjecture. Acta Mathematica, v. 198, p. 1-56, 2007.

43.
AVILA, A.;AVILA, ARTUR2007AVILA, A.; BOCHI, J. . A uniform dichotomy for generic SL(2,R) cocycles over a minimal base. Bulletin de la Société Mathématique de France, v. 135, p. 407-417, 2007.

44.
AVILA, A.;AVILA, ARTUR2007AVILA, A.; VIANA, M. . Simplicity of Lyapunov spectra: a sufficient criterion. Portugaliae Mathematica, v. 64, p. 311-376, 2007.

45.
AVILA, A.;AVILA, ARTUR2007AVILA, A.; BOCHI, J. . Generic expanding maps without absolutely continuous invariant sigma-finite measure. Mathematical Research Letters, v. 14, p. 721-730, 2007.

46.
AVILA, A.;AVILA, ARTUR2006 AVILA, A.; KRIKORIAN, R. . Reducibility or non-uniform hyperbolicity for quasiperiodic Schrodinger cocycles. Annals of Mathematics, v. 164, p. 911-940, 2006.

47.
AVILA, A.;AVILA, ARTUR2006AVILA, A.; GOUEZEL, S. ; Yoccoz, J.-C. . Exponential mixing for the Teichmüller flow. Publications Mathématiques. Institut des Hautes Études Scientifiques, v. 104, p. 143-211, 2006.

48.
AVILA, A.;AVILA, ARTUR2006AVILA, A.; BOCHI, J. . A generic C^1 map has no absolutely continuous invariant measure. Nonlinearity (Bristol), v. 19, p. 2717-2725, 2006.

49.
AVILA, A.;AVILA, ARTUR2006AVILA, A.; GOUEZEL, S. ; TSUJII, M. . Smoothness of solenoidal attractors. Discrete and Continuous Dynamical Systems. Series B, v. 15, p. 21-35, 2006.

50.
AVILA, A.;AVILA, ARTUR2005AVILA, A.; MOREIRA, C.G. . Statistical properties of unimodal maps: the quadratic family. Annals of Mathematics, v. 161, p. 831-881, 2005.

51.
AVILA, A.;AVILA, ARTUR2005 AVILA, A.; MOREIRA, C.G. . Statistical properties of unimodal maps: physical measures, periodic points and pathological laminations. Publications Mathématiques. Institut des Hautes Études Scientifiques, v. 101, p. 1-67, 2005.

52.
AVILA, A.;AVILA, ARTUR2005AVILA, A.; DAMANIK, D. . Generic singular spectrum for ergodic Schrödinger operators. Duke Mathematical Journal, v. 130, p. 393-400, 2005.

53.
AVILA, A.;AVILA, ARTUR2005AVILA, A.; VIANA, M. . Dynamics in the moduli space of Abelian differentials. Portugaliae Mathematica, v. 62, p. 531-547, 2005.

54.
AVILA, A.;AVILA, ARTUR2004AVILA, A.; BUFF, X. ; CHERITAT, A. . Siegel disks with smooth boundaries. Acta Mathematica, v. 193, p. 1-30, 2004.

55.
AVILA, A.;AVILA, ARTUR2004AVILA, A.; MOREIRA, C.G. . Quasisymmetric robustness of the Collet-Eckmann condition in the quadratic family. Bulletin of the Brazilian Mathematical Society, v. 35, p. 291-331, 2004.

56.
ABDENUR, F.2004ABDENUR, F. ; AVILA, A. ; BOCHI, J. . Robust transitivity and topological mixing for C^1-flows. Proceedings of the American Mathematical Society, v. 132, p. 699-705, 2004.

57.
AVILA, A.;AVILA, ARTUR2004AVILA, A.. Convergence of an exact quantization scheme. Communications in Mathematical Physics, v. 249, p. 305-318, 2004.

58.
AVILA, A.;AVILA, ARTUR2003 AVILA, A.; LYUBICH, M. ; DE MELO, W. . Regular or stochastic dynamics in real analytic families of unimodal maps. Inventiones Mathematicae, v. 154, p. 451-550, 2003.

59.
AVILA, A.;AVILA, ARTUR2003AVILA, A.; MOREIRA, C.G. . Statistical properties of unimodal maps: smooth families with negative Schwarzian derivative. Astérisque, v. 286, p. 81-118, 2003.

60.
AVILA, A.;AVILA, ARTUR2002AVILA, A.; BOCHI, J. . A formula with some applications to the theory of Lyapunov exponents. Israel Journal of Mathematics, v. 131, p. 125-137, 2002.

61.
AVILA, A.;AVILA, ARTUR2002AVILA, A.. Infinitesimal perturbations of rational maps. Nonlinearity (Bristol), v. 15, p. 695-704, 2002.



Orientações



Orientações e supervisões concluídas
Dissertação de mestrado
1.
Zhiyuan Zhang. Some problems on stationary measures and invariant measures. 2013. Dissertação (Mestrado em Matematica) - Université Paris Diderot, . Orientador: Artur Avila Cordeiro de Melo.

2.
Martin Leguil. Weak mixing properties of interval exchange transformations and translation flows. 2013. Dissertação (Mestrado em Matematica) - Université Paris Diderot, . Orientador: Artur Avila Cordeiro de Melo.

3.
Xu Disheng. Forced multiplicities of Lyapunov spectrum. 2012. Dissertação (Mestrado em Matematica) - Université Paris Diderot, . Orientador: Artur Avila Cordeiro de Melo.

Tese de doutorado
1.
Martin Leguil. Dynamique de cocycles et problemes de rigidite. 2017. Tese (Doutorado em Matematica) - Université Paris Diderot, . Orientador: Artur Avila Cordeiro de Melo.

2.
Xiaochuan Liu. Lyapunov Exponents Approximation, Symplectic Cocycle Deformation and a Large Deviation Theorem. 2016. Tese (Doutorado em Doutorado em Matemática) - Instituto Nacional de Matemática Pura e Aplicada, . Orientador: Artur Avila Cordeiro de Melo.

3.
Disheng Xu. Lyapunov exponents and rigidity. 2016. Tese (Doutorado em Matematica) - Université Paris Diderot, . Orientador: Artur Avila Cordeiro de Melo.

4.
Zhenghe Zhang. Positivity and continuity of Lyapunov exponents for one-frequency, smooth quasi-periodic Schrödinger operator. 2014. Tese (Doutorado em Doutorado em matematica) - Northwestern University, . Coorientador: Artur Avila Cordeiro de Melo.

5.
Maria Joao Resende. Exponential Decay for the Teichmuller Flow in the Moduli Space of Quadratic Differentials. 2009. Tese (Doutorado em Doutorado em Matemática) - Instituto Nacional de Matemática Pura e Aplicada, . Coorientador: Artur Avila Cordeiro de Melo.




Página gerada pelo Sistema Currículo Lattes em 21/10/2018 às 7:10:46