Pedro A. S. Salomão is a Visiting Professor of Mathematics at NYU Shanghai. Salomão is also a faculty member at the University of São Paulo. His research interests are largely toward understanding global properties of conservative dynamical systems, utilizing recently developed methods in symplectic topology. This research area has now been called Symplectic Dynamics. Salomão has been using pseudo-holomorphic curves to study the existence of global surfaces section and transverse foliations, constructing algebraic invariants that detect periodic orbits and, more recently, estimating systolic ratios of Reeb flows.
Global surfaces of section for Reeb flows in dimension three and beyond, Proceedings of the International Congress of Mathematicians 2018, 1, 937-964, 2019. (with U. Hryniewicz)
Sharp systolic inequalities for Reeb flows on the three-sphere, Inventiones Mathematicae v.211, 687-778, 2017. (with A. Abbondandolo, B. Bramham and U. L. Hryniewicz)
A Poincaré-Birkhoff theorem for tight Reeb flows on S^3. Inventiones Mathematicae, v. 199, 333-422, 2015. (with U. Hryniewicz and A. Momin)
Systems of transversal sections near critical energy levels of Hamiltonian systems in R^4. Memoirs of the American Mathematical Society v. 252 (1202), 1-105, 2018. (with N. de Paulo)