João Carlos Ferreira Costa

• Abstract

  The purpose of this work is to study importanttopics of Singularity theory such as nvariants, classification problem, finiteness theorems, stable maps, pairs of map germs (or divergent diagrams), among others. Such topics are interrelated with other areas of research, such as Differential Geometry, Topology, Dynamical System and Graph Theory. To develop this study, from local point of v…

  Invariants of real singularities, pairs of germs and classification problems, AP.R

• Abstract

  The research project is on the characteristic classes and intersection homology theory. The first subject to be investigated concerns Milnor classes. It is curious that, at the moment, there are few (or none) examples and applications of them. Another point on Milnor classes, is that the Prof. Brasselet gave a conjecture formula for duality of these classes in terms of polar varieties. No…

  Characteristic classes and intersection homology, AV.EXT

• Abstract

  The goal of this work is to study properties and invariants of bi-Lipchitz contact equivalence of smooth map-germs. This equivalence relation is the Lipschitz version of contact equivalence introduced by J. Mather. Few results exist on this subject in literature. (AU)

  Bi-Lipschitz contact equivalence of smooth map-germs, AP.R

• Abstract

  The goal of this work is to approach the study of curves and surfaces in the Minkowski space (or also called Lorentz-Minkowski space), having as a starting point the classic elements of Differential Geometry of curves and surfaces in the Euclidean space. We investigate what are the points which are affected or not bymetric change. Also, we want to know the differences and similarities bet…

  An introduction to differential geometry of curves and surfaces in Minkowski space, BP.IC

• Abstract

  The main goal of this work is to study the classification problem of singularities until codimension 5, up to R-equivalence. The contents of the project are based in a introductory course of Singularity Theory, which is not given in a regular course of Mathematics.

  Singularities of smooth function germs, BP.IC

• Abstract

  The main goal of this plan is to study aspects from the geometry and the topology of surfaces based in the beautiful Gauss-Bonnet theorem. In fact, the Gauss Bonnet theorem presents a good relationship between the geometry of the surface (the Gaussian curvature) and the topological aspects of the surface (Euler-Poincare characteristic). Some physical applications will be studied based on …

  The Gauss-Bonnet theorem, the Euler-Poincare characteristic and applications, BP.IC

(Only some records are available in English at this moment)