Hyperbolic geometry with applications to dynamics
to May 08, 2025
Location: Faculty of Math and Comp Science, historical building of Universitat de Barcelona (Gran Via 585)
Schedule: Tuesdays and Thursdays at 15:00, from 1st April 2025 to 8 May 2025
Free registration but mandatory through SIGN IN.
Introduction
Hyperbolic geometry deals with manifolds with conformal metrics of constant curvature -1. Despite this apparently narrow focus, it has found widespread applications in dynamical systems – mostly in the study of holomorphic dynamics, but also in relation to geodesic flows and its properties.
In this course, we will focus on the hyperbolic geometry of Riemann surfaces. We will introduce the hyperbolic metric of the unit disc and general hyperbolic surfaces, with an emphasis on the role of complex analysis and Möbius transformations. We will discuss the main structural properties for hyperbolic surfaces and their relations to Fuchsian groups and to holomorphic maps. Finally, we will see how to apply the principles of hyperbolic geometry to holomorphic dynamics and the study of geodesic flows.
This course is geared towards postgraduate students and early career researchers in mathematics with an interest in geometry, dynamics, or both.
Organising Committee & Speakers
Gustavo Rodrigues Ferreira
Centre de Recerca Matemàtica (CRM)
Gustavo Rodrigues Ferreira is a María de Maeztu postdoctoral fellow at the CRM working with the dynamical systems group. He completed his PhD at the Open University under the supervision of Phil Rippon and Gwyneth Stallard, and afterwards held short postdocs at Imperial College London and at the University of Liverpool.
His main research interests are holomorphic dynamics, geometric function theory, and applications of mathematics to the modelling of biological systems. His work focuses on wandering domains of entire and meromorphic functions, especially with regards to internal dynamics and parameter spaces.
Personal Website
Robert Cardona
Universitat de Barcelona (UB)
Robert Cardona is an assistant professor at the Universitat de Barcelona. He earned his Ph.D. in Mathematics at the Universitat Politècnica de Catalunya in 2021 and was awarded the Vicent Caselles prize from the Royal Spanish Mathematical Society. After his doctoral studies, he was a postdoctoral fellow at the Université de Strasbourg and the Instituto de Ciencias Matemáticas.
His research interests are mostly geometry, topology, and dynamical systems. His work centers on contact/symplectic topology, Hamiltonian dynamics, and geometric hydrodynamics. He is a member of the research project “Geometria i Topologia” and the principal investigator of the research project “Interactions between symplectic topology, hydrodynamics, and conservative flows.”
Personal Website
CONTENT
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Hyperbolic geometry in the unit disc
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Hyperbolic surfaces
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Fuchsian groups
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Applications to holomorphic dynamics
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Applications to geodesic flows
References
F. Dal’Bo. “Geodesic and Horocycle Trajectories”. Springer-Verlag, 2011.
LIST OF PARTICIPANTS
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LODGING INFORMATION
ON-CAMPUS AND BELLATERRA
BARCELONA AND OFF-CAMPUS
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For inquiries about this event please contact the Scientific Events Coordinator Ms. Núria Hernández at nhernandez@crm.cat
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