Curriculum Vitae Name : Artur Avila Cordeiro de Melo
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| Curriculum Vitae Name : Artur Avila Cordeiro de Melo. Born : June 29, 1979 - Rio de Janeiro - RJ - Brazil. Citizenship : Brazilian, French. Address : UP7D, Bˆ atiment Sophie Germain, Case 7012, 75205 PARIS Cedex 13, France. Instituto Nacional de Matem´ atica Pura e Aplicada, IMPA, Estrada Dona Castorina, 110, Rio de Janeiro, 22460-320, Brazil. Email : artur.avila@imj-prg.fr, avila@impa.br Internet sites : http ://www.impa.br/∼avila/, https ://www.imj-prg.fr/∼artur.avila/ PhD : IMPA, 2001. Jury : W. de Melo (advisor), M. Viana, J. Palis, J.-C. Yoccoz, J. Milnor. Current positions : Since 2008. Directeur de recherche at the CNRS. From 2008 to 2009. On leave. Since 2009. Attached to the Institut de Math´ ematiques de Jussieu-Paris Rive Gauche (UMR 7586, CNRS, Universit´ e Paris Diderot, UPMC). Since 2009. Researcher (C´ atedra Arm´ınio Fraga) at IMPA, CNRS UMI 2294. Previous positions : From 2001 to 2003. Maˆıtre de Conf´ erence Associ´ e at the Coll` ege de France. From 2003 to 2008. Charg´ e de recherche at the CNRS. From 2003 to 2006. Attached to the Laboratoire de Probabilit´ es et Mod` eles Al´ eatoires (UMR 7599, CNRS, Universit´ e Paris Diderot, UPMC). From 2006 to 2008. On leave. From 2006 to 2009. Research fellow of the Clay Mathematics Institute, attached to IMPA, CNRS UMI 2294. Prizes and honors Gold medal at the International Mathematical Olympiad, Canada, 1995. Cours Peccot at the Coll` ege de France, 2005. Invited address at the ICMP, 2006. Bronze medal of the CNRS, 2006. Salem prize, 2006. Wolff Memorial Lectures at Caltech, 2008. Invited address at the ECM, 2008 EMS prize, 2008. Grand Prix Jacques Herbrand of the French Academy of Sciences, 2009. Porter Lectures at Rice, 2010. Plenary address at the ICM, 2010. Blyth Lectures at Toronto, 2011. Michael Brin prize, 2011. IAMP Early Career Award, 2012. Prˆ
emio da SBM, 2013. TWAS Prize, 2013. Bellow Lectures at Northwestern, 2014. Fields Medal, 2014. TWAS-Lenovo Science Prize, 2015. Service
1 2 Editorial boards : Ergodic Theory and Dynamical Systems (current), Mathematical Proceedings of the Cambridge Philosophical Society, Publications Math´ ematiques de l’IHES, Duke Mathematical Journal. ERC Starting Grant (5 years, starting in 01/12/2010). Papers Published (1) On the dynamics of the renormalization operator. A. Avila, M. Martens, W. de Melo. In “Global Analysis of Dynamical Systems : Festschrift de- dicated to Floris Takens for his 60th birthday”, Ed. H.Broer, B. Krauskopf, G. Vegter, Institute of Physics Publishing, Bristol and Philadelphia, 2001, pp. 449–460. (2) Infinitesimal perturbations of rational maps. A. Avila. Nonlinearity 15 (2002), 695-704. (3) A formula with applications to the theory of Lyapunov exponents. A. Avila, J. Bochi. Israel Journal of Mathematics 131 (2002), 125-137. (4) Statistical properties of unimodal maps : smooth families with negative Schwarzian derivative. A. Avila, C. G. Moreira. Ast´ erisque 286 (2003), 81-118. (5) Regular or stochastic dynamics in real analytic families of unimodal maps. A. Avila, M. Lyubich, W. de Melo. Inventiones Mathematicae 154 (2003), 451-550. (6) Robust transitivity and topological mixing for C 1 -flows.
F. Abdenur, A. Avila, J. Bochi. Proceedings of the AMS 132 (2004), 699-705. (7) Convergence of an exact quantization scheme. A. Avila. Communications in Mathematical Physics 249 (2004), 305-318. (8) Quasisymmetric robustness of the Collet-Eckmann condition in the quadratic familly. A. Avila, C. G. Moreira. Bulletin of the Brazilian Mathematical Society 35 (2004), 291-331. (9) Siegel disks with smooth boundaries. A. Avila, X. Buff, A. Ch´ eritat. Acta Mathematica 193 (2004), 1-30. (10) Statistical properties of unimodal maps : the quadratic family. A. Avila, C. G. Moreira. Annals of Mathematics 161 (2005), 831-881. (11) Statistical properties of unimodal maps : physical measures, periodic orbits and pathological laminations. A. Avila, C. G. Moreira. Pub. Math. IH ´ ES 101 (2005), 1-67. (12) Generic singular spectrum for ergodic Schr¨ odinger operators. A. Avila, D. Damanik. Duke Mathematical Journal 130 (2005), 393-400. (13) Phase-Parameter relation and sharp statistical properties for general families of unimodal maps. A. Avila, C. G. Moreira. Contemporary Mathematics 389 (2005), 1-42. (14) Smoothness of solenoidal attractors. A. Avila, S. G¨ ouezel, M. Tsujii. Discrete and Continuous Dynamical Systems 15 (2006), 21-35. (15) Examples of Feigenbaum Julias sets with small Hausdorff dimension. A. Avila, M. Lyubich. In “Dynamics on the Riemann Sphere. A Bodil Branner Festschrift”, Ed. Poul G. Hjorth, Carsten Lunde Petersen, European Mathematical Society (EMS), Z¨ urich,
pp. 71-87, 2006. (16) A generic C 1 map has no absolutely continuous invariant measure. A. Avila, J. Bochi. Nonlinearity 19 (2006), 2917-2925. 3 (17) Reducibility or non-uniform hyperbolicity for quasiperiodic Schr¨ odinger cocycles. A. Avila, R. Krikorian. Annals of Mathematics 164 (2006), 911-940. (18) Exponential mixing for the Teichm¨ uller flow. A. Avila, S. Gou¨ ezel, J.-C. Yoccoz. Pub. Math. IH ´ ES 104 (2006), 143-211. (19) Weak mixing for interval exchange transformations and translation flows. A. Avila, G. Forni. Annals of Mathematics 165 (2007), 637-664. (20) Simplicity of Lyapunov spectra : proof of the Zorich-Kontsevich conjecture. A. Avila, M. Viana. Acta Mathematica 198 (2007), 1-56. (21) Generic expanding maps without absolutely continuous invariant σ-finite measure. A. Avila, J. Bochi. Mathematical Research Letters 14 (2007), 721-730. (22) Simplicity of Lyapunov spectra : a sufficient criterion. A. Avila, M. Viana. Portugaliae Mathematica 64 (2007), 311-376. (23) A uniform dichotomy for generic SL(2, R) cocycles over a minimal base. A. Avila, J. Bochi. Bulletin de la Soci´ et´
e Math´ ematique de France 135 (2007), 407-417. (24) Exponential decay of correlations for the Rauzy-Veech-Zorich renormalization map. A. Avila, A. Bufetov. Fields Institute Communications 51 (2007), 203-211. (25) Hausdorff dimension and conformal measures of Feigenbaum Julia sets. A. Avila, M. Lyubich. Journal of the American Mathematical Society 21 (2008), 305-363. (26) Absolute continuity of the integrated density of states for the almost Mathieu operator with non-critical coupling. A. Avila, D. Damanik. Inventiones Mathematicae 172 (2008), 439-453. (27) Cantor Spectrum for Schr¨ odinger Operators with Potentials arising from Generalized Skew- shifts.
A. Avila, J. Bochi, D. Damanik. Duke Mathematical Journal 146 (2009), 253-280. (28) On the spectrum and Lyapunov exponent of limit periodic Schr¨ odinger operators. A. Avila. Communications in Mathematical Physics 288 (2009), 907-918. (29) The ten martini problem. A. Avila, S. Jitomirskaya. Annals of Mathematics 170 (2009), 303-342. (30) Combinatorial rigidity for unicritical polynomials. A. Avila, J. Kahn, M. Lyubich, W. Shen. Annals of Mathematics 170 (2009), 783-797. (31) Nonuniform center bunching and the genericity of ergodicity among C 1 partially hyperbolic symplectomorphisms. A. Avila, J. Bochi, A. Wilkinson. Annales Scientifiques de l’Ecole Normale Superieure 42 (2009), 931-979. (32) Almost localization and almost reducibility. A. Avila, S. Jitomirskaya. Journal of the European Mathematical Society 12 (2010), 93-131. (33) Uniform exponential growth for some SL(2, R) matrix products. A. Avila, T. Roblin. Journal of Modern Dynamics 3 (2009), 549-554. (34) Density of positive Lyapunov exponents for quasiperiodic SL(2, R) cocycles in arbitrary dimen- sion. A. Avila. Journal of Modern Dynamics 3 (2009), 629-634. (35) Bulk universality and clock spacing of zeros for ergodic Jacobi matrices with a.c. spectrum. A. Avila, Y. Last, B. Simon. Analysis & PDE 3 (2010), 81-118. 4 (36) Extremal Lyapunov exponents : an invariance principle and applications. A. Avila, M. Viana. Inventiones Mathematicae 181 (2010), 115-174. (37) Uniformly hyperbolic finite-valued SL(2, R) cocycles. A. Avila, J. Bochi, J.-C. Yoccoz. Commentarii Mathematici Helvetici 85 (2010), 813-884. (38) On the regularization of conservative maps. A. Avila. Acta Mathematica 205 (2010), 5-18. (39) Parapuzzle of Multibrot sets and typical dynamics of unimodal maps. A. Avila, M. Lyubich, W. Shen. Journal of the European Mathematical Society 13 (2011), 27-56. (40) H¨
older continuity of absolutely continuous spectral measures for one-frequency Schr¨ odinger
operators. A. Avila, S. Jitomirskaya. Communications in Mathematical Physics 301 (2011), 563-581. (41) Cohomological equations and invariant distributions for minimal circle diffeomorphisms. A. Avila, A. Kocsard. Duke Mathematical Journal 158 (2011), 501-536. (42) Density of positive Lyapunov exponents for SL(2, R) cocycles. A. Avila. Journal of the American Mathematical Society 24 (2011), 999-1014.. (43) A KAM scheme for SL(2, R) cocycles with Liouvillean frequencies. A. Avila, B. Fayad, R. Krikorian. Geometric and Functional Analysis 21 (2011), 1001-1019. (44) Mixing for time-changes of Heisenberg nilflows. A. Avila, G. Forni, C. Ulcigrai. Journal of Differential Geometry 89 (2011), 369-410. (45) The full renormalization horseshoe for unimodal maps of higher degree : exponential contraction along hybrid classes. A. Avila, M. Lyubich. Publications Math´ ematiques de l’IH ´ ES 114 (2011), 171-223. (46) Nonuniform hyperbolicity, global dominated splittings and generic properties of volume-preserving diffeomorphisms. A. Avila, J. Bochi. Transactions of the American Mathematical Society 364 (2012), 2883-2907. (47) Opening gaps in the spectrum of strictly ergodic Schr¨ odinger operators. A. Avila, J. Bochi, D. Damanik. Journal of the European Mathematical Society 14 (2012) 61-106.
(48) Exponential Mixing for the Teichm¨ uller flow in the Space of Quadratic Differentials. A. Avila, M.J. Resende. Commentarii Mathematici Helvetici 87 (2012), 589-638. (49) Small eigenvalues of the Laplacian for algebraic measures on moduli space, and mixing properties of the Teichm¨ uller flow. A. Avila, S. Gou¨ ezel. Annals of Mathematics 178 (2013), 385-442. (50) SL(2,R)-invariant probability measures on the moduli spaces of translation surfaces are regular. A. Avila, C. Matheus, J.-C. Yoccoz. Geometric and Functional Analysis 23 (2013), 1705-1729. (51) Holonomy invariance : rough regularity and applications to Lyapunov exponents. A. Avila, J. Santamaria, M. Viana. Ast´ erisque 358 (2013), 13-74. (52) On rigidity of critical circle maps. A. Avila. Bulletin of the Brazilian Mathematical Society 44 (2013), 611-619. (53) Singular density of states measure for subshift and quasi-periodic Schr¨ odinger operators. A. Avila, D. Damanik, Z. Zhang. Communications in Mathematical Physics 330 (2014), 469-498. (54) Complex one-frequency cocycles. A. Avila, S. Jitomirskaya, C. Sadel. Journal of the European Mathematical Society 16 (2014), 1915-1935.
5 (55) On manifolds supporting distributionally uniquely ergodic diffeomorphisms. A. Avila, B. Fayad, A. Kocsard. Journal of Differential Geometry 99 (2015), 191-213. (56) On the Kotani-Last and Schr¨ odinger conjectures. A. Avila. Journal of the American Mathematical Society, 28 (2015) 579-616. (57) Absolute continuity, Lyapunov exponents and rigidity I : geodesic flows. A. Avila, M. Viana, A. Wilkinson. Journal of the European Mathematical Society 17 (2015), 1435-1462. (58) The visits to zero of a random walk driven by an irrational rotation. A. Avila, D. Dolgopyat, E. Duryev, O. Sarig. Israel Journal of Mathematics 207 (2015), 653-717. (59) Monotonic cocycles. A. Avila, R. Krikorian. Inventiones Mathematicae 202 (2015), 271-331. (60) Global theory of one-frequency Schr¨ odinger operators. A. Avila. Acta Mathematica 215 (2015), 1-54. (61) Weak mixing directions in non-arithmetic Veech surfaces. A. Avila, V. Delecroix. Journal of the American Mathematical Society 29 (2016), 1167-1208. (62) Towers for commuting endomorphisms, and combinatorial applications. A. Avila, P. Candela. Annales de l’Institut Fourier 66 (2016), 1529-1544. (63) An integrable deformation of an ellipse of small eccentricity is an ellipse. A. Avila, J. de Simoi, V. Kaloshin. Annals of Mathematics 184 (2016), 527-558. Accepted for publication (64) Recurrence for the wind-tree model. A. Avila, P. Hubert. To appear in : Annales de l’Institut Henri Poincar´ e-Analyse Non Lin´ eaire. (65) Symplectic and isometric SL(2, R) invariant subbundles of the Hodge bundle. A. Avila, A. Eskin, M. M¨ oller. To appear in : Journal f¨ ur die reine und angewandte Mathematik. (66) On the Hausdorff dimension of the Rauzy gasket. A. Avila, P. Hubert, A. Skripchenko. To appear in : Bulletin de la Soci´ et´
e Math´ ematique de France. (67) Diffusion for chaotic plane sections of 3-periodic surfaces. A. Avila, P. Hubert. S. Skripchenko. To appear in : Inventiones Mathematicae. (68) Diffeomorphisms with positive metric entropy. A. Avila, S. Crovisier, A. Wilkinson. To appear in : Publications Math´ ematiques de l’IHES. Submitted for publication (69) Statistical properties of quadratic polynomials with a neutral fixed point. A. Avila, D. Cheraghi. (70) On mixing diffeomorphisms of the disk. A. Avila, B. Fayad, P. Le Calvez, D. Xu, Z. Zhang. (71) Sharp Phase transitions for the almost Mathieu operator. A. Avila, J. You, Q. Zhou. (72) Zorich conjecture for hyperelliptic Rauzy-Veech groups. A. Avila, C. Matheus, J.-C. Yoccoz. (73) Spectral Theory of Extended Harper’s Model and a Question by Erds and Szekeres. A. Avila, S. Jitomirskaya, C. Marx. (74) Second phase transition line. A. Avila, S. Jitomirskaya, Q. Zhou.
6 (75) Lebesgue measure of Feigenbaum Julia sets. A. Avila, M. Lyubich. (76) Weak mixing properties of interval exchange transformations and translation flows. A. Avila, M. Leguil. Preprints (77) Smooth Siegel disks via semicontinuity : a remark on a proof of Buff and Cheritat. A. Avila. (78) The absolutely continuous spectrum of the almost Mathieu operator. A. Avila. (79) On point spectrum at critical coupling. A. Avila. (80) Distortion elements in Diff ∞ (R/Z). A. Avila. (81) Almost reducibility and absolute continuity I. A. Avila. (82) Some monoids of Pisot matrices. A. Avila, V. Delecroix. Expository (83) Bifurcations d’applications unimodales. A. Avila. C. R. Acad. Sci. Paris, Ser. I 334 (2002), 483-488. (84) Bifurcations of unimodal maps. A. Avila, C. G. Moreira. In Dynamical Systems. Part II : Topological Geometrical and Ergodic Properties of Dynamics. Publicazioni della Classe di Scienze, Scuola Normale Superieure, Pisa. Centro di Ricerca Matematica “Ennio De Giorgi” : Proceedings, 2003, pp. 1-22. (85) Dynamics in the moduli space of Abelian differentials. A. Avila, M. Viana. Portugaliae Mathematica 62 (2005), 531-547. (86) Solving the ten martini problem. A. Avila, S. Jitomirskaya. Lecture Notes in Physics 690 (2006), 5-16. (87) Chaoticity of the Teichm¨ uller flow. A. Avila. Clay Mathematics Proceedings 10 (2010), 321-338. (88) Dynamics of renormalization operators. A. Avila. In “Proceedings of the International Congress of Mathematicians 2010. Volume 1.” World Scientific Publishing, pp. 154-175. (89) Cocycles over partially hyperbolic maps. A. Avila, M. Viana, A. Wilkinson. Ast´ erisque 358 (2013), 1-12. Yüklə 84,57 Kb. Dostları ilə paylaş:
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