Infinitesimal Spaces of Quasiregular Mappings

Prof. Alastair Fletcher
Professor of Mathematical Sciences and Director of Undergraduate Studies
Northern Illinois University

How can we differentiate functions which are not differentiable? In the context of quasiregular mappings, a generalization of holomorphic functions where now infinitesimal circles are mapped to infinitesimal ellipses, there is a satisfactory answer to this question given by infinitesimal spaces. In this talk, we will survey these objects and discuss some ongoing work with relevance to the Decomposition Problem for bi-Lipschitz maps.