Dynamics and geometry in low dimensions

• Grant number: 23/07076-4
• Support Opportunities: Research Projects - Thematic Grants
• Duration: July 01, 2024 - June 30, 2029
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Fábio Armando Tal
• Grantee: Fábio Armando Tal
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Pesquisadores principais: André Salles de Carvalho ; Clodoaldo Grotta Ragazzo ; Edson de Faria ; Salvador Addas Zanata
• Associated researchers: Albert Meads Fisher ; Edson Vargas ; Ricardo dos Santos Freire Júnior

Abstract

The present pre-project continues the work of three previous Thematic Projects supported by FAPESP with numbers 2006/03829-2, 2011/16265-8, and 2016/25053-8. The research group includes established researchers working in dynamical systems and low-dimensional geometry. Younger researchers will be included later in the full project as associated researchers. The areas covered by the project are:Dynamics in dimension 2:a) Dynamics of homeomorphisms and diffeomorphisms of the torus.b) Topological and differentiable dynamics on surfaces.c) Henon transformations.Topology and geometry of 3-manifolds and connections with dynamics in dimension 2.Teichmuller theory and its connections with dynamics and geometry in low dimensions.Interval endomorphisms, critical circle transformations, renormalization, and parameter space.Continuous and differentiable ergodic theory of finite and infinite measures.The present proposal aims to continue the work we have been doing and also expand the activities of the group by attracting post-doctoral researchers, students, and visitors, as well as broadening the range of topics we have been working on. (AU)