Singularity theory has a wide range of applications to various areas of science and interacts with several lines of mathematics, including differential and algebraic geometry and qualitative theory of differential equations. It contributes to the development of knot theory, optics, robotics and computer vision. At the same time, these areas have enriched the singularity theory with problems and results of interest and relevance. The central themes of research of the singularity theory group include the development of methods of classification of singularities, of different applications and of real and complex analytic sets, with special attention to invariants and equisingularity conditions in families of such sets.

Since its beginning in the late 1960's, the group has a strong participation in the training of new researchers/professors and in the internationalization of research and graduate studies in mathematics at ICMC. Since the 1990s, it has been internationally consolidated as one of the most active in its area, through an intense exchange of researchers and graduate students with several research centers.

A traditional activity of the group is the organization of scientific meetings, among which the International Workshop on Real and Complex Singularities, which is an international event recognized by the scientific community as one of the leading periodic conference in the area, and the Mini Workshop on Singularities, Geometry and Differential Equations. Such meetings have a significant participation of the national and international scientific community in the area and provide a great interaction among researchers, young scientists and graduate students from Brazil and abroad. With good international projection, the group currently attracts for scientific visitors, PhD and postdoctoral internships.