Mathematics Graduate Students Organization

Seminar:

Date: January 27

Given a surface in Euclidean 3 space, one can define its Gauss map to the 2-sphere, where a point maps to its unit normal vector translated to the origin. For most surfaces, the image of this Gauss map is 2-dimensional, and a classical theorem states there are exactly two types of exceptions: if the surface is a cone, or the union of the set of tangent lines to a curve. I will review the classical theorem and then explain its surprising relation to the Clay prize problem P v. NP that comes from computer science. As a bonus I'll present some amazing formulas regarding the determinant that seem to have been previously unknown.