Whitney and His Umbrella - Exploring Singular Surfaces

Explore the concept of Whitney umbrellas in this one-hour mathematics seminar presented by Ton Marar from the Universidade de Sao Paulo. Delve into Hassler Whitney's observation about the singularities of smooth mappings from surfaces to three-dimensional space. Learn how slight alterations can reduce complex singularities to a single, tame type known as the Whitney umbrella. Examine the properties of semiregular maps and their resulting singular surfaces. Investigate the relationship between reduced defining equations and parametrizations of singular surfaces, gaining insights into this fundamental concept in differential topology.