# Jacob Pratscher

Northern Illinois University

**Talk Title: **A Realization of the Orbit Space

**Abstract: **Quasiregular mappings are guaranteed to be differentiable almost everywhere, meanwhile there is a concept of derivatives that holds everywhere, called a generalized derivative. The collection of generalized derivatives at a point is called the infinitesimal space. It is known that the infinitesimal space consists of one or uncountably many generalized derivatives. The orbit of a given point is defined as its image under all elements of a particular infinitesimal space. In this talk, we will fully classify the possibilities for the orbit, by explicitly constructing certain quasiconformal mappings.