Speaker: Les Wilson (UHM)
Title: Singularity Theory
Abstract: Singularity Theory studies singular phenomena in various fields: singular points of sets (where the set is not locally a manifold), singular points of functions (where the partial derivatives are all 0) or of mappings (where the Jacobian matrix is not maximal rank), singular points of vector fields or differential forms (where it is zero), singular points of geometric structures, etc. I will give examples, discuss common techniques (e.g. stability, genericity, finite determinacy, bifurcation), and some areas I’m particularly interested in.
Title : Harmonic functions on Sierpinski carpets
Abstract : I will discuss a notion of Sobolev spaces and harmonic functions on Sierpinski carpets, which differs from the classical approach of potential theory in metric measure spaces. The goal is to define a notion that takes into account also the ambient space, where the carpet lives. As an application of carpet-harmonic functions we obtain a quasisymmetric uniformization result for Sierpinski carpets.