I will first describe a new kind of geometric knot theory, where the knots in question are piecewise linear with segments only running parallel to axes. I will present an algorithm to list knot types with a fixed length, and thus in principle completely understand knotting in this setting. I will then move on to the notion of Vassiliev derivatives, extending the definition from collections of double-points to more general kinds of singularities. I will give some examples and then, time-permitting, address how this relates to unstable Vassiliev spectral sequences for plumbers' knots.n |