Faculty Profile

Education

• Doctor of Science in Applied Mathematics, University of São Paulo, 1999-2002.

• Master in Applied Mathematics, University of São Paulo, 1997-1999.

• Bachelor in Administration, Fundação Getúlio Vargas, 1994-1998.

• Mechatronics Engineering, University of São Paulo, 1992-1996.

Positions

• Professor at Sustech, 2023-.

• Visiting Professor at New York University - Shanghai, 2020-2023.

• Visiting Professor at Ruhr-Universität Bochum, 2018-2019.

• Associate Professor, Department of Mathematics, University of São Paulo, 2009-2023.

• Assistant Professor, Department of Mathematics, University of São Paulo, 2003-2009.

Publications

• Genus zero transverse foliations for weakly convex Reeb flows on the tight three-sphere, Advances in Mathematics, 2024.

• Genus zero global surfaces of section for Reeb flows and a result of Birkhoff, Journal of the European Mathematical Society, 2023.

• Global surfaces of section with positive genus for dynamically convex Reeb flows, Journal of Fixed Point Theory and Applications, 2022.

• Reeb flows, pseudo-holomorphic curves and transverse foliations, São Paulo Journal of Mathematical Sciences, 2022.

• Sharp systolic inequalities for Riemannian and Finsler spheres of revolution, Transactions of the American Mathematical Society, 2021.

• On the relation between action and linking, Journal of Modern Dynamics, 2021.

• Contact forms with large systolic ratio in dimension three, Annali della Scuola Normale Superiore de Pisa-Classe de Scienze, 2019.

• On the multiplicity of periodic orbits and homoclinics near critical energy levels of Hamiltonian systems in R⁴ , Transactions of the American Mathematical Society, 2019.

• Systolic ratio, index of closed orbits and convexity for tight contact forms on the three-sphere. Compositio Mathematica, 2018.

• Global surfaces of section for Reeb flows in dimension three and beyond, Proceedings of the International Congress of Mathematicians 2018, 2019.

• Systems of transversal sections near critical energy levels of Hamiltonian systems in R⁴ . Memoirs of the American Mathematical Society, 2018.

• Sharp systolic inequalities for Reeb flows on the three-sphere, Inventiones Mathematicae, 2017.

• A systolic inequality for geodesic flows on the two-sphere. Mathematische Annalen, 2017.

• Elliptic binding for dynamically convex Reeb flows on the real projective space. Calculus of Variations and Partial Differential Equations, 2016.

• A Poincaré-Birkhoff theorem for tight Reeb flows on S³ . Inventiones Mathematicae, 2015.

• A dynamical characterization of universally tight lens spaces. Proceedings of the London Mathematical Society, 2014.

• Persistence of fixed points under rigid perturbations of maps. Fundamenta Mathematicae, 2014.

• Global properties of tight Reeb flows with applications to Finsler geodesic flows on S² . Mathematical Proceedings of the Cambridge Philosophical Society, 2013.

• An almost existence theorem for non-contractible periodic orbits on cotangent bundles. São Paulo Journal of Mathematical Sciences, 2013.

• Introdução à Geometria Finsler. 1. ed. Rio de Janeiro: IMPA, 2013. 208p, in portuguese.

• A full family of multimodal maps on the circle. Ergodic Theory and Dynamical Systems, 2011.

• On the existence of disk-like global sections for Reeb flows on the tight 3-sphere. Duke Mathematical Journal, 2011.

• Uma introdução à geometria de contato e aplicações à dinâmica Hamiltoniana. 1. ed. Rio de Janeiro: IMPA, 2009. v. 1., 207p, in portuguese.

• Global surfaces of section in non-regular convex energy levels of Hamiltonian systems. Mathematische Zeitschrift, 2007.

• Equatorial dynamics of charged particles in planetary magnetospheres. Physica D, 2007.

• Assessing debt sustainability in Brazil. Brazilian Review of Econometrics, 2007.

• The Conley-Zehnder index and the saddle-center equilibrium. Journal of Differential Equations, 2006.

• The Thurston operator for semi-finite combinatorics. Discrete and Continuous Dynamical Systems, 2006.

• A Conjectura de Seifert: sobre a existência de órbitas periódicas de campos de vetores em S³ . Matemática Universitária, 2005.

• Convex energy levels of Hamiltonian systems. Qualitative Theory of Dynamical Systems, 2004.

• Homoclinic orbits near saddle-center fixed points of Hamiltonian systems with two degrees of freedom. Astérisque, 2003.