Topological invariants and geometric structures of mixed analytic varieties

• Grant number: 25/09846-7
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: January 01, 2026
• End date: December 31, 2028
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Bruna Orefice Okamoto
• Grantee: Inácio Augusto Rabelo Pinto
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

Mixed maps are real analytic mappings in complex variables and their conjugates. These maps spring in the context of Milnor fibration for real singularities and generalize several properties of the complex analogous. Since then, these have a central role in the research of the topology of singularities. In his thesis, the candidate developed a new geometric approach on contact structures and Lipschitz geometry of the analytic varieties determined by mixed maps, called mixed varieties. In this project, our purpose is to generalize this investigation to non-isolated mixed singularities and their topological invariants, especially from the deformations and Newton non-degeneracy points of view. Furthermore, with the goal to compare the analytic properties of the real and complex realms and to expand the frontiers between the many branches of Geometry and Topology, we will explore geometric structures in a large sense associated with the moment angle manifolds of mixed type. These remarkable spaces are of great interest in algebraic topology, non-Kähler geometry, and mathematical physics. (AU)