Abstract: This talk is the ninth lecture of the VISGRAF Seminar Series "Next Media for Storytelling: Fundamentals and State-of-the-Art".
We will focus on Expanded Cinema as the basis for a new language in the context of emerging media. The topics to be investigated include: Virtual Reality, Augmented Reality and Mixed Reality; Live CInema and Virtual Cinematograpy; as well as Alternative Interactive Viewing.
Hilbert Series Associated to Symplectic Quotients by SU2
Abstract: In this talk, we will present the Hilbert series of the graded algebra of real regular functions on the symplectic quotient associated to an SU2-module and an explicit expression for the first nonzero coefficient of the Laurent expansion of this Hilbert series at t = 1. We will provide an outline of the used techniques for our calculations, and will discuss some of our related results on Hilbert series. This is joint work with Hans-Christian Herbig (UFRJ) and Christopher Seaton (Rhodes College).
Singular integration towards a spectrally accurate finite difference
Abstract: It is an established fact that finite differences approximate derivatives with a fixed algebraic rate of convergence. Nevertheless, we exhibit a new finite difference scheme and prove it has spectral accuracy. Its rate of convergence is not fixed and improves with the function’s regularity. For example, the rate of convergence is exponential for analytic functions. Our new framework is conceptually nonstandard, making no use of polynomial interpolation, nor any other expansion basis, as typically considered in approximation theory. Our new method arises solely from the numerical manipulation of singular integrals, through an accurate quadrature for Cauchy Principal Value convolutions. The kernel is a distribution which gives rise to multi-resolution grid coefficients. The respective distributional finite difference scheme is spatially structured having stencils of different support widths. These multi-resolution stencils test/estimate function variations in a nonlocal fashion, giving rise to a highly accurate distributional finite difference scheme. Computational illustrations are presented, where the accuracy and roundoff error structure are compared with the respective Fourier based method.