This text presents an overview of Maria Aparecida Soares Ruas’s influential contributions to the study of equisingularity, especially her question from the mid-1990s about whether topological triviality and Whitney equisingularity coincide for families of parametrized surfaces in C³.
A central example in this development is Ruas surface, arising from a family of finitely determined holomorphic map-germs whose unfolding is topologically trivial but not Whitney equisingular — a phenomenon that challenged long-held expectations in the field.
Earlier work by Ruas and several collaborators had uncovered strong connections between invariants such as the Milnor number of the double point curve and the geometry of stable perturbations, yet the conjecture remained unresolved. The decisive breakthrough came in 2016, when Ruas and her student O. N. Silva constructed explicit counterexamples, establishing that topological triviality does not imply Whitney equisingularity even under constant double point Milnor number.
Ruas surface, the central fiber of this family, has since become a key example in the literature. More details can be found in this PDF file.
The cover video of this website was created by Aldício José Miranda (UFU, Brazil). The visualization of Ruas surface shown in the video was produced by him using 3D printing technology.