New Frontiers in Singularity Theory and Bi-Lipschitz Geometry of Semialgebraic Set...
Topological invariants of stable maps and classification of singularities
Qualitative theory of differential equations in the plane: topological classificat...
Abstract
Singularity theory has wide applications to various areas of mathematics and in particular to differential geometry and qualitative theory of differential equations. These branches of mathematics feedback, in turn, into and enrich singularity theory. The aim of this project is to develop methods of classification of real and complex singularities with special attention to invariants and equisingularity conditions for families of sets and mappings, and to apply singularity theory to problems in differential geometry and differential equations. The project, with well defined objectives, aims at consolidating research activities in the state of São Paulo in geometric aspects of dynamical systems and singularity theory. The interaction will promote the development in the following areas: 1) geometry and classification of singularities; 2) topology of singular sets and mappings; 3) algebraic methods in singularity theory; 4) singularities in differential geometry; 5) applications to bifurcation problems and to the qualitative theory of differential equations. (AU)
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