Organisers: RC Ball (Cambridge), KJ Falconer (St Andrews)
Over the past twenty years there has been an explosion of activity in developing the mathematics of fractals and applying fractals across science. More recently there has been increasing understanding of "multifractals", where more than one scaling exponent is involved. Despite these advances, on the mathematical side activity has been concentrated where rigorous work is tractable, particularly on 'static' problems, and on the physical side much activity has been merely 'fractal spotting', leaving a gulf between the mathematics and physical applications. This programme is concerned with topical aspects of the mathematics and applications of fractals. Our major aims are to encourage interaction between mathematicians and scientists with different approaches and viewpoints, to increase the awareness of scientists of the mathematics that is already available, and to focus the attention of mathematicians on areas where further theoretical development is needed.
The programme is expected to cover the following areas: problems of a 'dynamic' nature relating to physical problems, such as diffusions and PDEs on fractals or domains with fractal boundary; multifractal theory and its applications; geometric measure and integration theory, especially recent techniques such as tangent measures; characterisation and measurement of fractals, including alternatives to dimension (eg lacunarity); the identification of mathematically based protocols to identify that a structure is fractal along with how the mathematical theory 'in the limit' relates to finite scales; fractal and multifractal techniques in mathematical analysis; and fractal aspects of the distribution of galaxies.
Report: Download Report
Fubini-type theorems for general measure constructions
Authors: KJ Falconer, RD Mauldin
Examples illustrating the instability of packing dimensions of sections
Authors: KJ Falconer, M Jarvenpaa, P Mattila
Markov property of Kusuoka-Zhou's Dirichlet forms on self-similar sets
Authors: J Kigami
A version of $\Omega$ for which $ZFC$ can not predict a single bit
Authors: RM Solovay
Multifractal spectra of branching measure on a Galton-Watson tree
Authors: N-R Shieh, SJ Taylor
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