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Research at St Andrews

Kenneth John Falconer

Person

Kenneth John Falconer
Postal address:
School of Mathematics and
Statistics
North Haugh
St Andrews
United Kingdom

Email: kjf@st-andrews.ac.uk

Direct phone: +44 (0)1334 463733

Research overview

Personal website: http://www.mcs.st-andrews.ac.uk/~kenneth/

Kenneth's research falls within the broad area of mathematical analysis, and is concentrated around Fractal Geometry. He has written over 120 papes, on topics such as fractal and dimensional analysis of classes of sets and measures including self-affine sets and measures and vector-valued measures; geometrical properties (such as projections and intersections) of Hausdorff, box and packing dimensions; fractals in dynamical systems; fractal aspects of stochastic processes; partial differential equations on fractal domains; applications of fractals including to rainfall distributions and finance. He is particulary associated with 'Falconer's distance problem' and the introduction of 'affinity dimension' in the study of self-affine sets. Recent work includes the use of potential-theoretic methods to study box-counting dimensions, the introduction of intermediate dimensions and their properties, and the construction of self-stabilising processes. He has written five books, including Fractal Geometry - Mathematical Foundations and Applications which has become the standard text on the subject and Fractals - A Very Short Introduction, intended for a general readership.

 

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