THE NASH PROBLEM FOR ARC SPACES

Wednesday Oct 2nd Fine 214 6:00 pm

Abstract: In a 1968 preprint, John Nash asked some very interesting questions about the family of all arcs on algebraic or analytic surfaces and hypersurfaces. I illustrate these questions using the examples of the surfaces (xy=z^n) and (x^2+y^3=z^4).

I plan to end up with a series of open questions about 4-variable polynomials, that is, algebraic hypersurfaces in 4-space.