Abstract:

Starting with examples from first and second year calculus, we study singularities of projections of surfaces into Eucidean spaces of various dimensions. The singularity sets reveal a good deal about the structure of the surfaces, leading to statements about Euler characteristics, homology, cohomology, and a great result called the Whitney Duality Theorem. We can actually "see" the result. (This informal presentation will be a good background for the Colloquium Talk on Thursday afternoon.)