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Faculty Profile

Detailed information about our faculty member

Carlos Gustavo Tamm de Araujo Moreira

Carlos Gustavo Tamm de Araujo Moreira

Distinguished Visiting Professor
someemail@sustech.edu.cn

Research Interests

1. Dynamical Systems 2. Number Theory 3. Combinatorics

Research Areas:

  1. Dynamical Systems
  2. Number Theory
  3. Combinatorics

Prizes and Titles:

2018 Erdös award of the World Federation of National Mathematical Olympiads (WFNMC)

2017 Invitation to give a plenary lecture at the ICM 2018 in Brazil

2013 Invitation to give a lecture at the Dynamical Systems session of the ICM 2014 in South Korea

2012 Elected Fellow of TWAS

2010 TWAS Prize in Mathematics

2009 UMALCA Prize – III Latin-American Congress of Mathematicians - Santiago, Chile

2008 Affiliated Member of the TWAS, TWAS-ROLAC

2008 Full Member of the Brazilian Academy of Sciences (ABC)

2007 TWAS-ROLAC Prize for Young Scientists – Mathematics

2007 Socio de Honor de la Sociedad Cubana de Matemática y Computación - Holguín, Cuba

1996 Prize Young Scientist - 45 years of CNPq – Rio de Janeiro, Brasil

1990 V Olimpíada Iberoamericana de Matemática – Valladolid, Spain - First Prize

1990 31º International Mathematical Olympiad (XXXI IMO) - Beijing, China – Gold medal

1989 IV Olimpíada Iberoamericana de Matemática – Havana, Cuba – Gold medal

1989 30º International Mathematical Olympiad (XXXI IMO) -Braunschweig, Germany – Bronze medal

Publications:

    1. Moreira, Carlos; Zamudio, Alex; Erratum: A corrected proof of the scale recurrence lemma from the paper "Stable intersections of regular Cantor sets with large Hausdorff dimensions''. Ann. of Math. (2) 195 (2022), no. 1, 363–374.
    1. Davi Lima, Carlos Matheus, Carlos Gustavo Moreira, Sandoel Vieira, M∖L is Not Closed, International Mathematics Research Notices, Volume 2022, Issue 1, January 2022, Pages 265–311, https://doi.org/10.1093/imrn/rnaa096
    1. Lima, Davi; Matheus, Carlos; Moreira, Carlos Gustavo; Vieira, Sandoel M∖L near 3. Mosc. Math. J. 21 (2021), no. 4, 767–788.
    1. Matheus, Carlos; Moreira, Carlos Gustavo Diophantine approximation, Lagrange and Markov spectra, and dynamical Cantor sets. Notices Amer. Math. Soc. 68 (2021), no. 8, 1301–1311.
    1. Lima, Davi; Moreira, Carlos Gustavo Phase transitions on the Markov and Lagrange dynamical spectra. Ann. Inst. H. Poincaré Anal. Non Linéaire 38 (2021), no. 5, 1429–1459.
    1. Kohayakawa, Yoshiharu; Lee, Sang June; Moreira, Carlos Gustavo; Rödl, Vojtěch On strong Sidon sets of integers. J. Combin. Theory Ser. A 183 (2021), Paper No. 105490, 29 pp.
    1. Bednařík, Dušan; Marques, Diego; Moreira, Carlos Gustavo; Trojovský, Pavel On the maximal invariant set for the x2 −2 restricted to intervals. Proyecciones 40 (2021), no. 2, 305–312.
    1. Brasil, Jader E.; Lopes, Artur O.; Mengue, Jairo K.; Moreira, Carlos G. Quantum spin probabilities at positive temperature are Hölder Gibbs probabilities. Commun. Contemp. Math. 23 (2021), no. 1, Paper No. 1950050, 32 pp.
    1. Marques, Diego; Moreira, Carlos Gustavo On the exceptional set of transcendental functions with integer coefficients in a prescribed set: the problems A and C of Mahler. J. Number Theory 218 (2021), 272–287.
    1. Matheus, Carlos; Moreira, Carlos Gustavo . Fractal geometry of the complement of Lagrange spectrum in Markov spectrum. Comment. Math. Helv. 95 (2020), no. 3, 593–633.
    1. Alfaro Vigo, Daniel G.; Álvarez, Amaury C.; Chapiro, Grigori; García, Galina C.; Moreira, Carlos G. Solving the inverse problem for an ordinary differential equation using conjugation. J. Comput. Dyn. 7 (2020), no. 2, 183–208.
    1. Delecroix, Vincent; Matheus, Carlos; Moreira, Carlos Gustavo. Approximations of the Lagrange and Markov spectra. Math. Comp. 89 (2020), no. 325, 2521–2536.13. Moreira, Carlos Gustavo T.; Pacifico, Maria José; Romaña Ibarra, Sergio; Hausdorff Dimension, Lagrange and Markov Dynamical Spectra for Geometric Lorenz Attractors. Bull. Amer. Math. Soc. (N.S.) 57 (2020), no. 2, 269–292.
    1. Mauduit, Christian; Moreira, Carlos Gustavo . Entropy ratio for infinite sequences with positive entropy. Ergodic Theory and Dynamical Systems 40 (2020), 751-762.
    1. Marques, Diego ; Moreira, Carlos Gustavo . On exceptional sets of transcendental functions with integer coefficients: solution of a problem of Mahler. Acta Arith. 192 (2020), no. 4, 313–327
    1. Mauduit, Christian; Moreira, Carlos Gustavo . Complexity and fractal dimensions for infinite sequences with positive entropy. Commun. Contemp. Math. 21 (2019), no. 6, 1850068, 19 pp.
    1. Matheus, Carlos; Moreira, Carlos Gustavo . HD(M∖L)>0.353. Acta Arith. 188 (2019), no. 2, 183–208.
    1. Matheus, Carlos; Moreira, Carlos Gustavo . Markov spectrum near Freiman's isolated points in M∖L. J. Number Theory 194 (2019), 390–408.
    1. Marques, Diego ; Moreira, Carlos Gustavo . On a stronger version of a question proposed by K. Mahler. JOURNAL OF NUMBER THEORY, v. 194, p. 372-380, 2019.
    1. Moreira, Carlos Gustavo . Dynamical systems, fractal geometry and Diophantine approximations. Proceedings of the International Congress of Mathematicians—Rio de Janeiro 2018. Vol. I. Plenary lectures, 731–757, World Sci. Publ., Hackensack, NJ, 2018.
    1. Kohayakawa, Yoshiharu ; Lee, Sang June ; Moreira, Carlos Gustavo ; Rödl, Vojta . Infinite Sidon Sets Contained in Sparse Random Sets of Integers. SIAM JOURNAL ON DISCRETE MATHEMATICS, v. 32, p. 410-449, 2018.
    1. Moreira, Carlos Gustavo . Geometric properties of the Markov and Lagrange spectra. ANNALS OF MATHEMATICS, v. 188, p. 145-170, 2018.
    1. Matheus, Carlos ; Moreira, Carlos Gustavo .; Palis, Jacob. Non-uniformly hyperbolic horseshoes in the standard family. COMPTES RENDUS MATHEMATIQUE, v. 356(2), p. 146-149, 2018.
    1. Cerqueira, Aline ; Matheus, Carlos ; Moreira, Carlos Gustavo . Continuity of Hausdorff dimension across generic dynamical Lagrange and Markov spectra. Journal of Modern Dynamics, v. 12, p. 151-174, 2018.
    1. MARQUES, DIEGO ; Moreira, Carlos Gustavo . A note on a complete solution of a problem posed by K. Mahler. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, v. 98, p. 60-63, 2018.26. FERENCZI, SÉBASTIEN ; MAUDUIT, CHRISTIAN ; Moreira, Carlos Gustavo . An algorithm for the word entropy. THEORETICAL COMPUTER SCIENCE, v. 743, p. 1-11, 2018.
    1. LOPES, ARTUR O. ; MENGUE, JAIRO K. ; MOHR, JOANA ; MOREIRA, CARLOS G. . Large deviations for quantum spin probabilities at temperature zero. Stochastics and Dynamics, v. 18, p. 1850044, 2018.
    1. Matheus, Carlos ; Moreira, Carlos Gustavo . Markov spectrum near Freiman's isolated points in M --- L. JOURNAL OF NUMBER THEORY, v. 194, p. 390-408, 2018.
    1. Marques, Diego; Moreira, Carlos Gustavo; On variations of the Liouville constant which are also Liouville numbers. Proceedings of the Japan Academy. Series A Mathematical Sciences, v. 92, p. 39-40, 2016.
    1. Marques, Diego; Moreira, Carlos Gustavo; A positive answer for a question proposed by K. Mahler. Math. Ann. 368 (2017), no. 3-4, 1059–1062.
    1. Romaña Ibarra, Sergio A.; Moreira, Carlos Gustavo; On the Lagrange and Markov dynamical spectra, Ergodic Theory and Dynamical Systems 37 (2017), no. 5, 1570-1591.
    1. Bugeaud, Yann; Gustavo Moreira, Carlos; Variations autour d'un théorème métrique de Khintchine. (French) [Variations on a metric theorem of Khintchine] Bull. Soc. Math. France 144 (2016), no. 3, 507–538.
    1. Berger, Pierre; Moreira, Carlos Gustavo; Nested Cantor sets. Math. Z. 283 (2016), no. 1-2, 419–435.
    1. Marques, Diego; Moreira, Carlos Gustavo; On variations of the Liouville constant which are also Liouville numbers. Proc. Japan Acad. Ser. A Math. Sci. 92 (2016), no. 3, 39–40.
    1. Mauduit, Christian; Moreira, Carlos Gustavo; Phénomène de Moser-Newman pour les nombres sans facteur carré. (French) [Moser-Newman phenomenon for square-free numbers] Bull. Soc. Math. France 143 (2015), no. 3, 599–617.
    1. López, Jorge Erick; Moreira, Carlos Gustavo; A generalization of Marstrand's theorem for projections of cartesian products. Ann. Inst. H. Poincaré Anal. Non Linéaire 32 (2015), no. 4, 833–840.
    1. Contiero, André; Moreira, Carlos Gustavo T. de A.; Veloso, Paula M.; On the structure of numerical sparse semigroups and applications to Weierstrass points, J. Pure Appl. Algebra 219 (2015), no. 9, 3946–3957.
    1. Marques, Diego; Moreira, Carlos Gustavo; On a variant of a question proposed by K. Mahler concerning Liouville numbers. Bull. Aust. Math. Soc. 91 (2015), no. 1, 29–33.39. MOREIRA, C. G. T. A. . Fractal geometry and dynamical bifurcations. Proceedings of the International Congress of Mathematicians - Seoul 2014, vol. III – Invited Lectures, 647-659.
    1. MOREIRA, C. G. T. A. ; SMANIA, D. . Metric Stability for Random Walks (with applications in renormalization theory)..Frontiers in complex Dynamics (Celebrating John Milnor's 80th birthday), 261– 322, Princeton Math. Ser., 51, Princeton Univ. Press, Princeton, NJ, 2014.
    1. MOREIRA, C. G. T. A. ; LUCA, F. ; POMERANCE, C. On integers which are the sum of a power of 2 and a polynomial value. Boletim da Sociedade Brasileira de Matemática 45 (2014), no. 3, 559–574.
    1. MOREIRA, C. G. T. A. ; LIMA, Y. . A Marstrand theorem for subsets of integers. Combinatorics, probability & computing. , v.23, n.1, p.102 - 115, 2014.
    1. MOREIRA, C. G. T. A. ; MATHEUS, C. ; PUJALS, E. . Axiom A versus Newhouse phenomena for Benedicks-Carleson toy models. Annales Scientifiques de l’École Normale Supérieure 46 (2013), fascicule 6, p. 857-878, 2013.
    1. MOREIRA, C. G. T. A. ; HOPPEN, C. ; KOHAYAKAWA, Y. ; RÁTH, B. ; SAMPAIO, R. M. . Limits of permutation sequences. J. Combin. Theory Ser. B 103 (2013), No. 1, 93-113.
    1. MOREIRA, C. G. T. A., LABARCA, R., PUMARIÑO, A., RODRIGUEZ, J. A. . "On bifurcation sets for symbolic dynamics in the Milnor-Thurston world". Communications in Contemporary Mathematics 14 (2012), 16 p..
    1. MOREIRA, C. G. T. A. ; GARCIA, I . On bounded distortions of maps in the real line. Dynamical Systems 27 (2012), 501-506.
    1. MOREIRA, C. G. T. A. ; MAUDUIT, C. . Generalized Hausdorff dimensions of sets of real numbers with zero entropy expansion. Ergodic Theory and Dynamical Systems 32 (2012), 1073-1089.
    1. MOREIRA, C. G. T. A. ; BERGELSON, V. ; LEIBMAN, A. . From discrete- to continuous-time ergodic theorems. Ergodic Theory and Dynamical Systems 32 (2012), 383-426.
    1. MOREIRA, C. G. T. A. . There are no C^1-stable intersections of regular Cantor sets. Acta Mathematica 206 (2011), no. 2, 311-323 .
    1. MOREIRA, C. G. T. A. ; BUGEAUD, Y. . Sets of exact approximation order by rational numbers III. Acta Arithmetica 146 (2011), no. 2, 177-193 .
    1. MOREIRA, C. G. T. A. ; LIMA, Y. . A combinatorial proof of Marstrand's theorem for products of regular Cantor sets. Expo. Math. 29 (2011), no. 2, 231-239 .52. MOREIRA, C. G. T. A. ; HOPPEN, C. ; KOHAYAKAWA, Y. ; SAMPAIO, R. M. . Testing permutation properties through subpermutations. Theor. Comput. Sci. 412, No. 29, 3555-3567. (2011).
    1. MOREIRA, C. G. T. A. ; LIMA, Y. . Yet another proof of Marstrand's theorem. Bulletin of the Brazilian Mathematical Society 42 (2011), no. 2, 331-345 .
    1. MOREIRA, C. G. T. A. ; MAUDUIT, C. . Complexity of infinite sequences with zero entropy. Acta Arithmetica 142 (2010), 331-346 .
    1. MOREIRA, C. G. T. A. ; YOCCOZ, J.C. . Tangences homoclines stables pour des ensembles hyperboliques de grande dimension fractale. Annales Scientifiques de l'École Normale Supérieure, 43, fascicule 1, p. 1-68, 2010.
    1. MOREIRA, C. G. T. A. ; HOPPEN, C. ; KOHAYAKAWA, Y. ; SAMPAIO, R. M. . Property testing and parameter testing for permutations. Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms, 66–75, SIAM, Philadelphia, PA (2010).
    1. ARBIETO, A. ; MATHEUS, C. ; MOREIRA, C. G. T. A. The remarkable effectiveness of ergodic theory in number theory - Part I. Green-Tao theorem – Ensaios Matemáticos, 17, p. 1-71, 2009
    1. MOREIRA, C. G. T. A. ; RUAS, M. A. S. . The curve selection lemma and the Morse-Sard theorem. Manuscripta Mathematica 129, p. 401-408, 2009.
    1. ALON, N. ; KOHAYAKAWA, Y. ; MAUDUIT, C. ; MOREIRA, C. G. T. A. ; RODL, V. . Measures of pseudorandomness for finite sequences: typical values. Proceedings of the London Mathematical Society, v. 95(3), p. 778-812, 2007.
    1. MOREIRA, C. G. T. A., RODL, V., KOHAYAKAWA, Y., MAUDUIT, C., ALON, N. Measures of pseudorandomness for finite sequences: minimal values. Combinatorics, probability & computing. , v.15, n.1-2, p.1 - 29, 2006.
    1. MOREIRA, C. G. T. A., AVILA,A. Statistical properties of unimodal maps:the quadratic family. Annals of Mathematics. , v.161, n.2, p.827 - 877, 2005.
    1. MOREIRA, C. G. T. A., AVILA,A. Phase-parameter relation and sharp statistical properties for general families of unimodal maps. Contemporary mathematics. , v.389, p.1 - 42, 2005.
    1. MOREIRA, C. G. T. A., AVILA,A. Statistical properies of unimodal maps:physical measures, periodic orbits and pathological laminations. Publications Mathématiques de L'Institut des Hautes Études Scientifiques. , v.101, n.1, p.1 - 67, 2005.
    1. MOREIRA, C. G. T. A., LABARCA, R. Essential dynamics for Lorenz maps on the real line and the lexicographical world. Annales de L´Institut Henri Poincaré-Analyse Non Linéaire. , 2005.
    1. MOREIRA, C. G. T. A., POURBARAT, M., HONARY, B. Stable intersections of affine Cantor sets. Boletim da Sociedade Brasileira de Matemática. , v.36, n.3, p.363 378, 2005.
    1. MOREIRA, C. G. T. A., KOHAYAKAWA, Y. Bounds for Optimal Coverings. Discrete Applied Mathematics. , v.141, n.1-3, p.263 - 276, 2004.
    1. MOREIRA, C. G. T. A., AVILA,A. Quasisymmetric robustness of the Collet-Eckmann condition in the quadratic family. Boletim da Sociedade Brasileira de Matemática. , v.35, n.2, p.291 - 331, 2004.
    1. MOREIRA, C. G. T. A., AVILA,A. Statistical properies of unimodal maps:smooth families with negative Schwarzian derivative. Astérisque. , v.286, p.81 - 118, 2003. Geometric Methods in Dynamics (I) - Volume in honor of Jacob Palis Welington de Melo - Marcelo Viana Jean-Christophe Yoccoz (Ed.)
    1. MOREIRA, C. G. T. A., MUNOZ, E. Sums of Cantor sets whose sum of dimensions is close to one. Nonlinearity. , v.16, n.5, p.1641 - 1647,

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    1. MOREIRA, C. G. T. A., AVILA,A. Bifurcations of unimodal maps. Pubblicazioni del Centro De Giorgi. , p.1 - 22, 2003. In Dynamical Systems, Part II: Topological Geometrical and Ergodic Properties of Dynamics.'' Pubblicazioni della Classe di Scienze, Scuola Normale Superieure, Pisa. Centro di Ricerca Matematica Ennio De Giorgi'': Proceedings.
    1. MOREIRA, C. G. T. A., KOHAYAKAWA, Y., RODL, V., MAUDUIT, C. Measures of pseudorandomness for finite sequences: minimum and typical values. TUCS General Publication. Turku: , p.159 - 169, 2003. Proceedings of WORDS'03 (Turku Cent. Comput. Sci., Turku)
    1. MOREIRA, C. G. T. A., LABARCA, R. Bifurcation of the essential dynamics of Lorenz maps and applications to Lorenz-like flows:contributions to the study of the expanding case. Boletim da Sociedade Brasileira de Matemática. , v.32, n.2, p.107 - 144,

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    1. MOREIRA, C. G. T. A., LABARCA, R. Bifurcations of the essential dynamics of Lorenz maps on the real line and the bifurcation scenario for the linear family. Scientia - Series A - Mathematical Sciences - New Series. , v.7, p.13 - 29, 2001.
    1. MOREIRA, C. G. T. A. Hausdorff measures and the Morse-Sard theorem. Publicacions Matematiques. Barcelona: , v.45, p.149 - 162, 2001.
    1. MOREIRA, C. G. T. A. Maximal invariant sets for restrictions of unimodal and tent maps. Qualitative Theory Of Dynamical Systems. , v.2, n.2, p.385 - 398, 2001.
    1. MOREIRA, C. G. T. A., YOCCOZ, J.C. Stable intersections of regular Cantor sets with large Hausdorff dimensions. Annals Of Mathematics. , v.154, n.1, p.45 - 96, 2001. (with a Corrigendum: "Stable intersections of regular Cantor sets with large Hausdorff dimensions", published em Annals of Mathematics (2) 154 (2001), no. 2, 527)
    1. MOREIRA, C. G. T. A., KOHAYAKAWA, Y. Bounds for optimal coverings. Electronic Notes in Discrete Mathematics. , 2001. http://www.elsevier.nl/gej-ng/31/29/24/39/23/show/Products/notes/index.htt Proceedings of the Brazilian Symposium on Graphs, Algorithms and Combinatorics (GRACO 2001)
    1. MOREIRA, C. G. T. A., BATES, S. M. Des nouvelles perspectives sur le Théorème de Morse-Sard. Comptes Rendus des Seances de l´Académie des Sciences de Paris - Serie I - Mathematique. , v.332, p.13 - 17, 2001.
    1. MOREIRA, C. G. T. A., PALIS, J., VIANA, M. Homoclinic tangencies and fractal invariants in arbitrary dimension/Tangences homoclines et invariants fractaux en dimension arbitraire. Comptés Rendus de L´Académie des Sciences Serie I - Mathematique. Paris: , v.333, n.5, p.475 - 480, 2001.
    1. MOREIRA, C. G. T. A., EMANUEL, P. An extremal problem in the hypercube and optimization of asynchronous circuits. European Journal of Combinatorics. , v.21, n.4, p.529 - 531, 2000.
    1. MOREIRA, C. G. T. A., RIVERA, J., MUNOZ, E. On the topology of arithmetic sums of regular Cantor sets. Nonlinearity. , v.13, n.6, p.2077 - 2087, 2000.
    1. MOREIRA, C. G. T. A. Sums of regular Cantor sets, dynamics and applications to number theory. Periodica Mathematica Hungarica. , v.37, n.1, p.55 - 63, 1998.
    1. MOREIRA, C. G. T. A., BAMON, R., PLAZA, S., VERA, J. Differentiable structures of central Cantor sets. Journal Ergodic Theory Dynamical Systems. , v.17, n.5, p.1027 - 1042, 1997.
    1. MOREIRA, C. G. T. A. On asymptotic estimates for arithmetic cost functions. Proceedings of the American Mathematical Society. , v.125, n.2, p.347 - 353, 1997.
    1. MOREIRA, C. G. T. A. Stable intersections of Cantor sets and homoclinic bifurcations. Annales de l'Institut Henri Poincaré - Analyse Non Linéaire. IHP, v.13, n.6, p.741 - 781, 1996.