Home

# A study of the geometric and algebraic sewing operations

 dc.contributor.supervisor Schippers, Eric (Mathematics) en dc.contributor.author Penfound, Bryan dc.date.accessioned 2010-09-10T23:09:40Z dc.date.available 2010-09-10T23:09:40Z dc.date.issued 2010-09-10T23:09:40Z dc.identifier.uri http://hdl.handle.net/1993/4162 dc.description.abstract The sewing operation is an integral component of both Geometric Function Theory and Conformal Field Theory and in this thesis we explore the interplay between the two fields. We will first generalize Huang's Geometric Sewing Equation to the quasi-symmetric case. That is, given specific maps g(z) and f^{-1}(z), we show the existence of the sewing maps F_{1}(z) and F_{2}(z). Second, we display an algebraic procedure using convergent matrix operations showing that the coefficients of the Conformal Welding Theorem maps F(z) and G(z) are dependent on the coefficients of the map phi(z). We do this for both the analytic and quasi-symmetric cases, and it is done using a special block/vector decomposition of a matrix representation called the power matrix. Lastly, we provide a partial result: given specific maps g(z) and f^{-1}(z) with analytic extensions, as well as a particular analytic map phi(z), it is possible to provide a method of determining the coefficients of the complementary maps. en dc.format.extent 751946 bytes dc.format.mimetype application/pdf dc.language.iso en_US dc.rights info:eu-repo/semantics/openAccess dc.subject algebraic sewing en dc.subject geometric sewing en dc.subject conformal field theory en dc.subject geometric function theory en dc.subject convergent matrix operations en dc.title A study of the geometric and algebraic sewing operations en dc.type info:eu-repo/semantics/masterThesis dc.degree.discipline Mathematics en dc.contributor.examiningcommittee Zorboska, Nina (Mathematics) Shamseddine, Khodr (Physics and Astronomy) en dc.degree.level Master of Science (M.Sc.) en dc.description.note October 2010 en
﻿