CURRICULUM VITAE. Carlos Matheus Silva Santos CURRENT POSITION AND PREVIOUS AFFILIATIONS
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1 CURRICULUM VITAE Carlos Matheus Silva Santos PERSONAL DATA Name: Carlos Matheus Silva Santos Date of birth: May 1st, 1984 Birthplace: Aracaju - SE - Brazil ACADEMIC DEGREES B. Sc. in Mathematics at UFRJ - Universidade Federal do Rio de Janeiro (2005). M. Sc. in Mathematics at IMPA - Instituto de Matemática Pura e Aplicada (2000) under the direction of prof. Carlos Gustavo Moreira. Ph.D. in Mathematics at IMPA (2004). Advisor: prof. Marcelo Viana. Thesis: Contributions to the ergodic theory of non-hyperbolic systems. Habilitation at Univ. Paris 13 (2017). Thesis: Quelques contributions à la théorie de l action de SL(2,R) sur les espaces de modules de surfaces plates. CURRENT POSITION AND PREVIOUS AFFILIATIONS Directeur de Recherche (DR2) (since October 2018) at CNRS CMLS, École Polytechnique Palaiseau Cedex, France Tel.: carlos.matheus@math.cnrs.fr Web: Chargé de Recherches ( ) at LAGA, CNRS - Univ. Paris 13 ATER PostDoc ( ) at Collège de France under the direction of prof. Jean-Christophe Yoccoz ANR PostDoc ( ) at Collège de France under the direction of prof. Jean- Christophe Yoccoz CNPq PostDoc ( ) at IMPA under the direction of prof. Marcelo Viana PARTICIPATIONS IN EDITORIAL BOARDS Survey editor for Ergodic Theory and Dynamical Systems (since March 2016). 1
2 REFEREE Referee for the journals: TEACHING Acta Mathematica, Advances in Mathematics, Algebraic and Geometric Topology, Annals of Mathematics, Annales Scientifiques de l École Normale Supérieure, Annales de l Institut Fourier, Annales de l Institut Henri Poincaré (Analyse non Linéaire), Astérisque, Bulletin de la SMF, Bulletin of the American Mathematical Society, Bulletin of the Brazilian Mathematical Society, Bulletin of the London Mathematical Society, Commentarii Mathematici Helvetici, Duke Mathematical Journal, Dynamics of Partial Differential Equations, Electronic Journal of Combinatorics, Ergodic Theory & Dynamical Systems, Experimental Mathematics, Fundamenta Mathematicae, Geometric and Functional Analysis, Geometry and Topology, Inventiones Mathematicae, Israel Journal of Mathematics, Journal of the American Mathematical Society, Journal of the Institute of Mathematics of Jussieu, Journal de Mathématiques Pures et Appliquées, Journal of Modern Dynamics, Journal of Statistical Physics, Mathematical Proceedings of the Cambridge Philosophical Society, Mathematical Research Letters, Mathematische Nachrichten, Nonlinearity and Pure and Applied Mathematics Quarterly. Course: Riemann surfaces (August November 2006); Institution: IMPA. Course: Introduction to Teichmüller theory and its applications to dynamics of interval exchange transformations, flows on surfaces and billiards (July 4 15, 2011). Taught together with prof. Giovanni Forni. Institution: Banach Center, Bedlewo, Poland. 2
3 Course: Birkhoff sums for interval exchange maps: the Kontsevich-Zorich cocycle (May 21 June 1, 2012). Taught together with prof. Jean-Christophe Yoccoz. Institution: ICTP, Trieste, Italy. Course: Dynamics of the Weil-Petersson geodesic flow (November 25 29, 2013). Taught together with prof. Keith Burns and prof. Boris Hasselblatt. Institution: CIRM, Luminy, France. Course: Introduction to the dynamics of the Teichmüller flow (August November 2015); Institution: IMPA. Course: The Lagrange and Markov spectra from the dynamical point of view (October 17 & 19, 2016). Institution: CIRM, Luminy, France. Course: Exposants de Lyapunov (October-December 2016); Institution: Univ. Paris 7. Course: Surfaces à petits carreaux et leurs exposants de Lyapunov (January- February 2017); Institution: Univ. Paris 13. Course: Surfaces à petits carreaux (November-December 2017); Institution: Univ. Paris 7. Course: Part time professor (since 2017/2018) at École Polytechnique. Course: Square-tiled surfaces (June 11 13, 2018). Institution: Institut Fourier, Grenoble, France. M.SC, PhD AND POST-DOCTORAL STUDENTS Supervision of Elise Goujard s M.SC. stage (ENS Cachan, France). Revêtements cycliques à petits carreaux (2011). Memoir: Co-advisor of Rodolfo Gutiérrez (Univ. Paris 7). Ph.D thesis co-directed with prof. Anton Zorich (Univ. Paris 7) since September Supervision of the post-doctoral visit of of Mauricio Poletti for one-year at LAGA (Univ. Paris 13) since January ORGANIZATION OF EVENTS Co-organizer with L. Marchese, T. Monteil and A. Sportiello of Journées de Géométrie et Combinatoire dans les Espaces des Modules (September 24 25, 2018), Université Paris 13, Villetaneuse, France. Co-organizer with J. Chaika and J. Tao of Summer School on Teichmüller Theory and its Connections to Geometry, Topology and Dynamics (August 20 24, 2018) Fields institute, Toronto, Canada. Co-organizer with P. Berger and S. Crovisier of A conference in memory of Jean- Christophe Yoccoz (May 29 June 1, 2017), Collège de France, Paris, France. Co-organizer with A. Avila, S. Crovisier, J. Palis, M. Viana and J.-C. Yoccoz of the International Conference on Dynamical Systems (July 4 8, 2016), Búzios, RJ, Brazil. Co-organizer with C. Mauduit, C. Moreira, Y. Lima and J.-C. Yoccoz of the 2nd Workshop on Combinatorics, Number Theory and Dynamical Systems (August 24 28, 2015), IMPA, Rio de Janeiro, Brazil. 3
4 Co-organizer with Sylvain Crovisier of the Third Palis-Balzan International Symposium on Dynamical Systems (June 14 20, 2015), Institut Henri Poincaré, Paris, France. Co-organizer with Luca Marchese of the Journée Surfaces Plates (May 20, 2015), Université Paris 13, Villetaneuse, France. Co-organizer with Sylvain Crovisier of the Second Palis-Balzan International Symposium on Dynamical Systems (June 10 14, 2013), Institut Henri Poincaré, Paris, France. Co-organizer with Yuri Lima, Christian Mauduit, Carlos Gustavo Moreira and Jean-Christophe Yoccoz of the Workshop on Combinatorics, Number Theory and Dynamical Systems (August 19 23, 2013), Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil. SEMINARS Co-organizer with C. Favre and T. Gauthier of the seminar DynamiX ( ), École Polytechnique, France. Co-organizer with G. Forni and A. Zorich of the seminar Géométrie et dynamique dans les espaces de modules ( ), Institut Henri Poincaré, Paris, France. Co-organizer with A. Zorich of the seminar Géométrie et dynamique dans les espaces de modules ( ), Institut Henri Poincaré, Paris, France. Co-organizer with G. Forni, J.-C. Yoccoz and A. Zorich of the seminar Géométrie et dynamique dans les espaces de modules ( ), Institut Henri Poincaré, Paris, France. PUBLICATIONS Equilibrium states for random non-uniformly expanding maps, joint with Alexander Arbieto and Krerley Oliveira. Nonlinearity, vol. 17, (2004). Abundance of stable ergodicity, joint with Christian Bonatti, Marcelo Viana and Amie Wilkinson. Commentarii Mathematici Helvetici, vol. 79, (2004). Decidability of chaos for some families of dynamical systems, joint with A. Arbieto. Foundations of Computational Mathematics, vol. 4, (2004). The Bernoulli property for weakly hyperbolic systems, joint with A. Arbieto and Maria Pacífico. J. Statistical Physics, vol. 117, p (2004). Immersions with fractal set of points of zero Gauss-Kronecker curvature, joint with A. Arbieto and K. Oliveira. Bulletin of the Brazilian Mathematical Society, vol.35, p (2004). Geometrical versus Topological Properties of Manifolds, joint with K. Oliveira. Journal of the Institute of Mathematics of Jussieu, vol. 4, p (2005). Rough solutions for the periodic Schrödinger - Korteweg-deVries system, joint with A. Arbieto and Adán Corcho. Journal of Differential Equations, vol.230, p (2006). 4
5 Global well-posedness of NLS-KdV systems for periodic functions, Electronic Journal of Differential Equations, vol. 2007, p (2007). A pasting lemma and some applications for conservative systems (a.k.a. A pasting lemma I: the vector field case ), joint with A. Arbieto, Ergodic Theory and Dynamical Systems, vol. 27, p (2007). On the periodic Schrödinger-Debye equation, joint with A. Arbieto, Communications in Pure and Applied Analysis, vol. 7, p (2008). Global well-posedness and non-linear stability of periodic traveling waves for a Schrödinger-Benjamin-Ono system, joint with Jaime Angulo and Didier Pilod, Communications in Pure and Applied Analysis, vol. 8, n.3, (2009). Sharp bilinear estimates and well-posedness for the 1D Schrödinger-Debye system, joint with Adán Corcho, Differential and Integral Equations, vol. 22, n.3-4, (2009). Well-posedness for the 1D Zakharov-Rubenchik system, joint with Felipe Linares, Advances in Differential Equations, vol. 14, n.3-4, (2009). The action of the affine diffeomorphisms on the relative homology group of certain exceptionally symmetric origamis, joint with Jean-Christophe Yoccoz, Journal of Modern Dynamics, vol. 4, n.3, (2010). Square-tiled cyclic covers, joint with Giovanni Forni and Anton Zorich, Journal of Modern Dynamics, vol. 5, n.2, (2011). Other relevant examples: appendix to G. Forni s article A geometric criterion for the non-uniform hyperbolicity of the Kontsevich-Zorich cocycle, Journal of Modern Dynamics, vol. 5, n.2, (2011). Some quantitative versions of Ratner s mixing estimates, Bulletin Brazilian Mathematical Society, vol. 44, (2013). SL(2,R)-invariant probability measures on the moduli spaces of translation surfaces are regular, joint with Artur Avila and Jean-Christophe Yoccoz, Geometric and Functional Analysis, v. 23, p (2013). Axiom A versus Newhouse phenomena for Benedicks-Carleson toy models, joint with Carlos Gustavo Moreira and Enrique Pujals, Annales Scientifiques de l École Normale Supérieure, vol. 46, n. 6, p (2013). Explicit Teichmüller curves with complementary series, joint with Gabriela Weitze- Schmithüsen, Bulletin de la Société Mathématique de France, vol. 141, n. 4, (2013). Lyapunov spectrum of invariant subbundles of the Hodge bundle, joint with Giovanni Forni and Anton Zorich, Ergodic Theory and Dynamical Systems, vol. 34, n. 2, (2014). Zero Lyapunov exponents of the Hodge bundle, joint with Giovanni Forni and Anton Zorich, Commentarii Mathematici Helvetici, vol. 89, n. 2, (2014). Homology of origamis with symmetries, joint with Jean-Christophe Yoccoz and David Zmiaikou, Annales de l Institut Fourier, vol. 64, (2014). 5
6 Un contre-exemple à la réciproque du critère de Forni pour la positivité des exposants de Lyapunov du cocycle de Kontsevich-Zorich, joint with Vincent Delecroix, Mathematical Research Letters vol. 22, p (2015). A coding-free simplicity criterion for the Lyapunov exponents of Teichmüller curves, joint with Alex Eskin, Geometriae Dedicata, vol. 179, n. 1, (2015). Hodge-Teichmüller planes and finiteness results for Teichmüller curves, joint with Alex Wright, Duke Mathematical Journal, vol. 164, (2015). Some examples of isotropic SL(2,R)-invariant subbundles of the Hodge bundle, joint with Gabriela Weitze-Schmithüsen, International Mathematics Research Notices, vol. 2015, n. 18, (2015). A criterion for the simplicity of the Lyapunov spectrum of square-tiled surfaces, joint with Martin Möller and Jean-Christophe Yoccoz, Inventiones mathematicae, vol. 202, n. 1, (2015). Typical symplectic locally constant cocycles over certain shifts of countable type have simple Lyapunov spectra, joint with Michel Cambrainha, Portugaliae Mathematica, vol. 73, n. 3, (2016). Rates of mixing for the Weil-Petersson geodesic flow I: No rapid mixing in nonexceptional moduli spaces, joint with Keith Burns, Howard Masur and Amie Wilkinson, Advances in Mathematics, vol. 306, p (2017). Rates of mixing for the Weil-Petersson geodesic flow: exponential mixing in exceptional moduli spaces, joint with Keith Burns, Howard Masur and Amie Wilkinson, Geometric and Functional Analysis, vol. 27, p (2017). Positivity of the top Lyapunov exponent for cocycles on semisimple Lie groups over hyperbolic bases, joint with Mário Bessa, Jairo Bochi, Michel Cambrainha, Paulo Varandas and Disheng Xu, Bulletin Brazilian Mathematical Society, vol. 49, no. 1, (2018). An estimate on the Hausdorff dimension of stable sets of non-uniformly hyperbolic horseshoes, joint with Jacob Palis, Discrete Contin. Dyn. Syst., vol. 38, (2018). Quaternionic covers and monodromy of the Kontsevich-Zorich cocycle in orthogonal groups, joint with Giovanni Forni and Simion Filip, Journal of the European Mathematical Society, vol. 20, (2018). Non-uniformly hyperbolic horseshoes in the standard family, joint with Carlos Gustavo Moreira and Jacob Palis, C. R. Acad. Sc., vol. 356, (2018). Zorich conjecture for hyperelliptic Rauzy-Veech groups, joint with Artur Avila and Jean-Christophe Yoccoz, Math. Annalen vol. 370, (2018). Symbolic dynamics for non-uniformly hyperbolic surface maps with discontinuities, joint with Yuri Lima, Annales de l ENS, vol. 51, 1-38 (2018). Continuity of Hausdorff dimension across generic dynamical Lagrange and Markov spectra, joint with Aline Cerqueira and Carlos Gustavo Moreira, Journal of Modern Dynamics, vol. 12, (2018). 6
7 BOOKS HD(M \ L) > 0.353, joint with Carlos Gustavo Moreira, to appear in Acta Arithmetica (2018). Appendix On special Lagrangian fibrations in generic twistor families of K3 surfaces, joint with Nicolas Bergeron, to the article Counting Special Lagrangian Fibrations in Twistor Families of K3 surfaces of Simion Filip, to appear in Annales de l ENS (2018). Markov spectrum near Freiman s isolated points in M \ L, joint with Carlos Gustavo Moreira, Journal of Number Theory, vol. 194, (2019). The Kontsevich-Zorich cocycle over Veech-McMullen family of symmetric translation surfaces, joint with Artur Avila and Jean-Christophe Yoccoz, Journal of Modern Dynamics, Veech special volume (2019). Aspectos ergódicos da teoria dos números (Ergodic aspects of Number Theory), joint with A. Arbieto and Carlos Gustavo Moreira, Publicações Matemáticas do IMPA - 26 o Colóquio Brasileiro de Matemática (2007). The remarkable efectiveness of Ergodic Theory in Number Theory, Parts I and II, (Part I together with A. Arbieto and Carlos Gustavo Moreira), Ensaios Matématicos vol. 17, p (2009). Dynamical Aspects of Teichmüller Theory, Atlantis Studies in Dynamical Systems, vol. 7, Springer International Publishing (2018). EXPOSITORY ARTICLES Disquisitiones Mathematicae ( mathematical blog. C 1 density of hyperbolicity for Benedicks-Carleson toy models, joint with Carlos Gustavo Moreira and Enrique Pujals, Oberwolfach Reports, vol. 6, p (2009). On the neutral Oseledets bundle of Kontsevich-Zorich cocycle over certain cyclic covers, joint with Giovanni Forni and Anton Zorich, Oberwolfach Reports, vol. 8, p (2011). Le flot géodésique de Teichmüller et la géométrie du fibré de Hodge, Actes du Séminaire de Théorie Spectrale et Géométrie du Institut Fourier à Grenoble, vol. 29, p ( ). Fractal geometry of non-uniformly hyperbolic horseshoes, Proceedings of the Ergodic Theory Workshops at University of North Carolina at Chapel Hill, , Ed. by Idris Assani, p (2013). A criterium for the simplicity of Lyapunov exponents of origamis, joint with Martin Möller and Jean-Christophe Yoccoz, Oberwolfach Reports, vol. 10, p (2013). Introduction to Teichmller theory and its applications to dynamics of interval exchange transformations, flows on surfaces and billiards, joint with Giovanni Forni, Journal of Modern Dynamics, vol. 8, no. 3/4, p (2014). 7
8 Lecture notes on the dynamics of the Weil-Petersson flow, CIRM Jean-Morlet Chair Subseries, B. Hasselblatt ed., Lect. Notes Math. 2164, , Springer Verlag (2017). Variations of Hodge structures, Lyapunov exponents and Kontsevichs formula, appendix to the book Gauss-Manin Connection in Disguise (Calabi-Yau Modular Forms) by Hossein Movasati, Surveys of Modern Mathematics, vol. 13 (2017). Les blogs: un outil dynamique de communication en mathématiques, Gazette des Mathématiciens, vol. 148, p (2016). The Lagrange and Markov spectra from the dynamical point of view, CIRM Jean- Morlet Chair Subseries, S. Ferenczi, J. Kulaga-Przymus, M. Lemanczyk (eds), Lect. Notes Math., vol 2213, , Springer, Cham (2018). October 16, Carlos Matheus Silva Santos 8
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