Titles and Abstracts

M. Bowick. A defect approach to distributions on the sphere: universal grain boundaries.
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Steven B. Damelin. Discrepancy estimates on spheres.
This talk will detail work of the author dealing with Koksma-Hlawka formulas on spheres. This work is in progress.

P. Grabner. Distribution Measures for Pointsets on the Sphere.
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D. Hardin and E. Saff. Minimal Riesz Energy Point Configurations for Rectifiable d-Dimensional Manifolds.
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K. Hesse. Lower Bounds for Cubature on the Sphere in Sobolev Spaces.
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M. Lai. Spherical Splines for Scattered Data Fitting and Interpolation.
We describe a computational method to find spherical spline interpolation and fitting to any given scattered data set using spherical splines of degree d and smoothness r for any d > r >= 0. The spherical splines are those splines introduced in Alfeld, Neamtu and Schumaker '96. For a better approximation, we show how to use splines of both even and odd degrees. For a more efficient computation, we propose a domain decomposition method to compute a spherical spline fitting locally to approximate the global spherical spline fitting.

N. Lain Fernandez. Polynomial Interpolation on the Sphere.
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Q. Le Gia. Continuous and discrete least square error estimates on spheres.
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P. Leopardi. The Coulomb Energy of Spherical Designs on S2.
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H. Mhaskar. Quadrature formulas on the sphere.
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P. Petrushev. Smoothness spaces on the sphere.
The Besov and Triebel-Lizorkin spaces on the n-dimensional sphere will be discussed. A new characterization of the B- and F-spaces will be given. The emphasis will be placed on the Besov spaces involved in the theory of nonlinear approximation on the sphere.

J. Prestin. A positive quadrature rule on the sphere.
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M. Reimer. Truncated Generalized Hyperinterpolation.
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L. Schumaker. Modelling the Earth's Gravitational Field with Spherical Splines.
Modelling the gravitational field of the earth is an important problem in Geodesy. Currently the field is modelled using a single spherical harmonic expansion with about 10000 terms. In this talk we discuss the use of tensor spherical splines to model the field. This produces a model based on locally supported functions which is much easier to update and evaluate.

I. Sloan. Approximation and point distribution on the sphere: view from down-under.
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P. Sutcliffe. Solitons, Fullerenes and Rational Maps between Spheres.
The study of soliton models of nuclei leads to connections with Fullerenes and yields an interesting problem concerning minimal energy rational maps between Riemann spheres. These aspects will be described and some recent results presented.

R. Womersley. Extreme Spherical Designs.
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J. Xiao. The Isoperimetric and Sobolev Inequalities Split.
Either the isoperimetric inequality or its equivalent Sobolev inequality in the Euclidean space is split into two stronger inequalities (with precise constants) involving either the Hausdorff capacity or its associated Choquet integral.

Y. Xu. Polynomial Interpolation on the Unit Sphere
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