Kenneth John Falconer

FRSE Fellowship of the Royal Society of Edinburgh (FRSE) is an award granted to individuals that the Royal Society of Edinburgh, Scotland's national academy of science and letters, judged to be "eminently distinguished in their subject". This soci ...

(born 25 January 1952) is an English

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

working in

mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (m ...

and in particular on

fractal geometry In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illus ...

. He is

Regius Professor of Mathematics The Regius Professorship of Mathematics is the name given to three chair (academic), chairs in mathematics at British universities, one at the University of St Andrews, founded by Charles II of England, Charles II in 1668, the second one at the Uni ...

in the School of Mathematics and Statistics at the

University of St Andrews (Aien aristeuein) , motto_lang = grc , mottoeng = Ever to ExcelorEver to be the Best , established = , type = Public research university Ancient university , endowment ...

. He is known for his work on the mathematics of

fractals In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illus ...

and in particular sets and measures arising from

iterated function systems In mathematics, iterated function systems (IFSs) are a method of constructing fractals; the resulting fractals are often self-similar. IFS fractals are more related to set theory than fractal geometry. They were introduced in 1981. IFS fractal ...

, especially

self-similar __NOTOC__ In mathematics, a self-similar object is exactly or approximately similar to a part of itself (i.e., the whole has the same shape as one or more of the parts). Many objects in the real world, such as coastlines, are statistically se ...

and self-affine sets. Closely related is his research on Hausdorff and other

fractal dimension In mathematics, more specifically in fractal geometry, a fractal dimension is a ratio providing a statistical index of complexity comparing how detail in a pattern (strictly speaking, a fractal pattern) changes with the scale at which it is meas ...

s. He formulated ''

Falconer's conjecture In geometric measure theory, Falconer's conjecture, named after Kenneth Falconer, is an unsolved problem concerning the sets of Euclidean distances between points in compact d-dimensional spaces. Intuitively, it states that a set of points that is ...

'' on the dimension of distance sets and conceived the notion of a

digital sundial A digital sundial is a clock that indicates the current time with numerals formed by the sunlight striking it. Like a classical sundial, the device contains no moving parts. It uses no electricity nor other manufactured sources of energy. The di ...

. In combinatorial geometry he established a lower bound of 5 for the chromatic number of the plane in the Lebesgue measurable case. Falconer was born at Bearsted Memorial Maternity Hospital outside

Hampton Court Palace Hampton Court Palace is a Grade I listed royal palace in the London Borough of Richmond upon Thames, southwest and upstream of central London on the River Thames. The building of the palace began in 1514 for Cardinal Thomas Wolsey, the chie ...

. He was educated at

Kingston Grammar School Kingston Grammar School is an independent co-educational day school in Kingston upon Thames, England. The school was founded by Royal Charter in 1561 but can trace its roots back to at least the 13th century.

Kingston upon Thames Kingston upon Thames (hyphenated until 1965, colloquially known as Kingston) is a town in the Royal Borough of Kingston upon Thames, southwest London, England. It is situated on the River Thames and southwest of Charing Cross. It is notable as ...

and

Corpus Christi College, Cambridge Corpus Christi College (full name: "The College of Corpus Christi and the Blessed Virgin Mary", often shortened to "Corpus"), is a constituent college of the University of Cambridge. From the late 14th century through to the early 19th century ...

. He graduated in 1974 and completed his

PhD PHD or PhD may refer to: * Doctor of Philosophy (PhD), an academic qualification Entertainment * '' PhD: Phantasy Degree'', a Korean comic series * ''Piled Higher and Deeper'', a web comic * Ph.D. (band), a 1980s British group ** Ph.D. (Ph.D. albu ...

in 1979 under the supervision of Hallard Croft. He was a research fellow at

from 1977–1980 before moving to

Bristol University , mottoeng = earningpromotes one's innate power (from Horace, ''Ode 4.4'') , established = 1595 – Merchant Venturers School1876 – University College, Bristol1909 – received royal charter , type ...

. He was appointed Professor of Pure Mathematics at the

University of St Andrews (Aien aristeuein) , motto_lang = grc , mottoeng = Ever to ExcelorEver to be the Best , established = , type = Public research university Ancient university , endowment ...

in 1993 and was head of the School of Mathematics and Statistics from 2001-2004. He was elected a Fellow of the

Royal Society of Edinburgh The Royal Society of Edinburgh is Scotland's national academy of science and letters. It is a registered charity that operates on a wholly independent and non-partisan basis and provides public benefit throughout Scotland. It was established i ...

in 1998. He served on the council of the

London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical S ...

from 2000-2009 including as publications secretary from 2006-2009. In 2020 he was awarded the

Shephard Prize The Shephard Prize is awarded by the London Mathematical Society to a mathematician or mathematicians for making a contribution to mathematics with a strong intuitive component which can be explained to those with little or no knowledge of univer ...

of the London Mathematical Society. His recreational interests include long-distance walking and hill walking. He was chair of the

Long Distance Walkers Association The Long Distance Walkers Association (LDWA) is a British not for profit, volunteer-led association whose aim is "to further the common interests of those who enjoy long distance walking". The LDWA is an association of people with the common inte ...

from 2000–03 and editor of their journal ''Strider'' from 1987–92 and 2007-12. In 2021 he was appointed a Vice President of the LDWA. He has twice climbed all the

Munro A Munro () is defined as a mountain in Scotland with a height over , and which is on the Scottish Mountaineering Club (SMC) official list of Munros; there is no explicit topographical prominence requirement. The best known Munro is Ben Nevis ...

s as well as all the

Corbetts This is a list of Corbett mountains in Scotland by height. Corbetts are defined as Scottish mountains between in height with a prominence over ; solely imperial measurement thresholds. The first list was compiled in the 1920s by John Rooke Co ...

References

Selected publications

* * * * *

External links

Personal web page
* {{DEFAULTSORT:Falconer, Kenneth 1952 births Living people 20th-century British mathematicians 21st-century British mathematicians Fellows of Corpus Christi College, Cambridge Alumni of Corpus Christi College, Cambridge Fellows of the Royal Society of Edinburgh Academics of the University of St Andrews People educated at Kingston Grammar School British geometers Functional analysts