Oct

10

Tue

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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.

Oct

17

Tue

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Oct

27

Fri

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.

Oct

31

Tue

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.

## University of Hawaiʻi at Mānoa