Title : Conformal welding homeomorphisms.
Abstract : Conformal welding is a correspondence between circle homeomorphisms and curves in the plane. It has appeared over the years to be of considerable interest in several areas of mathematics and applications, such as Teichmüller Theory, Kleinian Groups, computer vision and pattern recognition, and so forth.
The uniqueness of conformal welding has been known for a long time to be closely related to the notion of conformal removability. In fact, many papers in the literature claim, using the same argument, that uniqueness is characterized precisely by the removability of the curve. In this talk, I will show that this argument is actually incorrect, so that the problem of characterizing uniqueness of conformal welding remains open.
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Title: Composition semigroups on spaces of analytic functions
Abstract : A semigroup {phi_t}_{t geq 0} of analytic self-maps of the disk satisifies phi_t circ phi_s = phi_{t+s}, and induces a semigroup of composition operators. We study the maximal space of strong continuity when the composition operators act on spaces of analytic functions, particularly H^{infty}, BMOA, and the Bloch space. We show that not every composition semigroup is strongly continuous on BMOA, answering a question that had remained open in the literature since at least 1998. This is joint work with Wayne Smith and Mirjana Jovovic.
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Speaker: Michelle Manes
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.