Prof Kenneth Falconer
Regius Chair of Mathematics
 Phone
 +44 (0)1334 46 3733
 kjf@standrews.ac.uk
 Office
 304 MI
 Location
 Mathematical Institute
Biography
Personal website: http://www.mcs.standrews.ac.uk/~kenneth/
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 eleected 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 (19992001) and Head of the School of Mathematics and Statistics (200104). 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 reserach programmes at the Isaac Newton Insitute and the MittagLeffler 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 (200003) and Editor of their journal Strider 198792, 200712) and was elected VicePresident in 2021. He has completed 35 of the LDWA's 100 mile cross country nonstop ultrawalking events.
Teaching
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 l 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.
Research areas
Personal website: http://www.mcs.standrews.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 selfaffine sets and measures and vectorvalued 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 selfaffine sets. Recent work includes the use of potentialtheoretic methods to study boxcounting dimensions, the introduction of intermediate dimensions and their properties, and the construction of selfstabilising 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.
PhD supervision
 Amlan Banaji
 Liam Stuart
 Alex Rutar
 Boyuan Zhao
Selected publications

Open access
Boxcounting dimension in onedimensional random geometry of multiplicative cascades
Falconer, K. J. & Troscheit, S., 18 Nov 2022, (Epub ahead of print) In: Communications in Mathematical Physics. First Online, 27 p.Research output: Contribution to journal › Article › peerreview

Open access
Intermediate dimension of images of sequences under fractional Brownian motion
Falconer, K. J., Mar 2022, In: Statistics and Probability Letters. 182, 6 p., 109300.Research output: Contribution to journal › Article › peerreview

Open access
Intersections of thick compact sets in ℝ^{d}
Falconer, K. & Yavicoli, A., Jul 2022, In: Mathematische Zeitschrift. 301, 3, p. 22912315 25 p.Research output: Contribution to journal › Article › peerreview

Open access
Minkowski dimension for measures
Falconer, K. J., Fraser, J. & Käenmäki, A., 29 Nov 2022, (Epub ahead of print) In: Proceedings of the American Mathematical Society. Early View, 15 p.Research output: Contribution to journal › Article › peerreview

Open access
Obituary  Richard Kenneth Guy, 19162020
Falconer, K. J., Feb 2022, In: Bulletin of the London Mathematical Society. 54, 1, p. 318333 16 p.Research output: Contribution to journal › Article › peerreview

Open access
The density of sets containing large similar copies of finite sets
Falconer, K., Kovač, V. & Yavicoli, A., 17 Nov 2022, (Epub ahead of print) In: Journal d'Analyse Mathématique. First Online, 19 p.Research output: Contribution to journal › Article › peerreview

Open access
The fractal structure of elliptical polynomial spirals
Burrell, S. A., Falconer, K. J. & Fraser, J., 1 Sep 2022, In: Monatshefte für Mathematik. 199, p. 122Research output: Contribution to journal › Article › peerreview

Open access
A capacity approach to box and packing dimensions of projections of sets and exceptional directions
Falconer, K. J., 8 Mar 2021, In: Journal of Fractal Geometry. 8, 1, p. 126 26 p.Research output: Contribution to journal › Article › peerreview

Open access
Assouad dimension influences the box and packing dimensions of orthogonal projections
Falconer, K. J., Fraser, J. & Shmerkin, P., 2021, In: Journal of Fractal Geometry. 8, 3, p. 247–259Research output: Contribution to journal › Article › peerreview

Open access
Intermediate dimensions  a survey
Falconer, K. J., 2021, Thermodynamic Formalism: CIRM JeanMorley Chair, Fall 2019. Pollicott, M. & Vaienti, S. (eds.). Cham: Springer, p. 469493 20 p. (Lecture Notes in Mathematics; vol. 2290).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution