Tropical aspects of singularities – SINTROP

The aim of this project is to foster interactions between the rapidly developing felds of tropical geometry, Berkovich analytic geometry and the theory of singularities. We are mainly interested in singularities of real and complex varieties, be they algebraic, analytic or formal. We will explore from various viewpoints the structure of non-archimedean links of singularities and study with tropical tools the Milnor fbers of smoothings of singularities, with a special emphasis on Newton non-degenerate embeddings of singularities. Our work will allow us to make substantial progress on several important but little explored general problems of singularity theory, among which we emphasize the following three: carry out a systematic study of the category of finite morphisms between singularities; construct new topological types of smoothings of real singularities of arbitrary dimension; construct explicit Newton non-degenerate embeddings of singularities. This will have automatically significant consequences in the metric and dynamical study of singularities, as well as in the development of new interactions of singularity theory with contact topology and symplectic topology.