Kenneth John Falconer


  • KY16 9SS

    United Kingdom

Accepting Postgraduate Research Students

Personal profile

Research overview

Personal website:

Kenneth's research falls within the broad area of mathematical analysis, and is concentrated around Fractal Geometry. He has written over 130 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.


Teaching activity

Kenneth lectures and tutors for mathematics courses at all levels, especially in mathematical analysis, including advanced courses in Fractal Geometry, Functional Analysis, Measure Theory, Probability, Analysis, Foundations of Mathematics, etc.. He also teaches regularly for entry level courses, following the Scottish tradition that new students have lectures from senior staff. He is a lecturer in Analysis for postgraduates as part of the Scottish Mathematics and Statistics Training Centre (SMSTC) which is video linked across Scotland. He supervises dissertations of about 6 undergraduates and 1 MSc student each year.

Kenneth has supervised 15 PhD students most of whom have gone on to academic careers.

He introduced the first Fractal Geometry course into the undergraduate curriculum in 1988, and similar courses have followed in many universities based on his book Fractal Geometry - Mathematical Foundations and Applications. He also designed and coordinated an Evening Degree module on Topics in Contemporary Mathematics, to introduce mature students with minimal mathematics to modern ideas.

He is a Fellow of the Higher Education Academy. 


Personal website:

Kenneth studied for the Mathematical Tripos at Corpus Christi College, Cambridge, where he graduated as a Wrangler in 1974. He gained a distinction in Part III of the Tripos in 1975 and went on get a PhD in Cambridge in 1977 with a thesis Properties of convex sets and functions determined by sectional integrals. He was elected a Research Fellow of Corpus Christi College in 1977.

He became a Lecturer in Mathematics at the University of Bristol in 1980 and was made a Reader in 1988. In 1993 he was appointed Professor in Pure Mathematics at the University of St Andrews where he went on to become the Senior (longest standing) Professor in the University. In 2017 the Queen appointed him Regius Professor of Mathematics at St Andrews. He was elected Fellow of the Royal Society of Edinburgh in 1998. He was awarded the Shephard Prize of the London Mathematical Society in 2020.

Kenneth has written 5 books and over 120 papers on various topics in mathematics, including many related to fractal geometry. He has spoken on his research at many national and international meetings.

University duties undertaken by Kenneth include Postgraduate ProDean (1999-2001) and Head of the School of Mathematics and Statistics (2001-04). He has served on various professional bodies, including the London Mathematical Society as Council Member, Publications Secretary, and Chair of the Nominating Commitee. He has been on the editorial boards of the LMS Bulletin, Journal and Proceedings, Advances in Mathematics, Journal of Fractal Geometry, and the Mathematical Proceedings of the Cambridge Philosophical Society. He has organised several major conferences and meetings, including as Chair of the British Mathematical Colloquium in 2018, and major researach programmes at the Isaac Newton Insitute and the Mittag-Leffler Institute.

Kenneth's main leisure activity is long distance walking and hill walking. He has twice climbed all the Munros as well as all the Corbetts. He was Chair of the Long Distance Walkers Asoociation (2000-03) and Editor of their journal Strider (1987-92, 2007-12, 2022-23) and was elected Vice-President in 2021. He has completed 35 of the LDWA's 100 mile cross country non-stop ultra-walking events.



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