Welcome to the SPOCK Home Page
About the Project
SPOCK (Scientific Properties of Complex Knots)
is a Research Programme Grant awarded by the Leverhulme Trust, and is a collaboration between
Durham University and the University of Bristol.
The aim of the project is to create new computational tools and mathematical techniques for the analysis,
synthesis and exploitation of knotted structures in a wide range of complex physical phenomena.
We are committed to involving the wider community, including the general public, in the work we are doing.
See public outreach for further details.
Whilst current information is updated regularly, we also keep a record of previous activities.
Please refer to our archive section for details of past events.
Contact details for people associated with the programme can be found on our
For information from the SPOCK team in Bristol, please see:
SPOCK Bristol Group
Publications and Outputs
We will provide details of related published papers as they become available.
Information about these publications and other research outputs, can be found on our
More about knots.....
Mathematically, a knot is a closed curve in three-dimensional space. A mathematician's knot therefore differs form knots in daily life, in that the ends must be joined together, so that the knot cannot be untied. A circle is the simplest example, but because it isn't knotted it is known as the unknot. The fundamental problem in knot theory is to determine whether a given closed curve is knotted. This unknotting problem, and more generally the identification of knots, leads to deep mathematical connections throughout the natural sciences.
Formation of Knotted Structures in Chemistry
The formation of molecular knots is a common phenomenon in chemistry. Prominent examples include DNA and even certain proteins.
Currently, we are investigating dynamical knot formation in excitable media, such as knots of concentrations
in the Belousov-Zhabotinsky reaction - a fascinating, oscillating reaction (see picture on the right).
We study both their mathematical modelling as well as experimental realisation. We are also interested in knot formation within supramolecular materials,
like gels. Gels are formed from many smaller molecules, called gelators.We're interested to see how these gelators arrange themselves to form a gel and how they can knot together.
Light-Matter Interaction with Knotted Light
We study the physics of knotted light fields interacting with dilute atomic vapours.
We are investigating ways to map the topologically complex properties of the light field onto
the state of the atomic ensemble, both theoretically and experimentally.
Knots in Anthropology
We investigate the evolution of knot diversity observed in human material culture.
Our aim is to develop a suitable mathematical framework to characterise variation in knots,
and investigate the processes of innovation and cultural transmission that gave rise to them.
The cultural evolution of knotting will be addressed through a combination of mathematical,
statistical and phylogenetic modelling, in addition to experiments simulating the cultural transmission of knot tying.