Measures of “badness” of singular points on hypersurfaces

Our talk is focused on singular points of hypersurfaces. By a hypersurface, we mean the set of solutions to a single polynomial equation in finitely many variables; a singular point of a hypersurface is one where the hypersurface fails to be smooth, e.g., a cusp or sharp corner. Intuitively, it is clear that some singular points are worse than others. We’ll discuss some approaches to putting a precise measure on how “bad” a singular point can be, and compare such approaches for polynomials with complex coefficients with others for polynomials with coefficients coming from finite fields. We’ll present lots of examples, as well as some open problems and recent progress.

There will be a reception immediately following the talk in the Math Common Room, Science Center – 4th Floor