# CAKE: Curvature - Applications - Knots - Energies

Curvature based geometric functionals have received great attention during the past years. Many 'energy' functionals defined on curves and surfaces have been investigated that aim at relating analytical properties to the geometry and topology of the respective objects. So-called knot energies play a central rôle in *geometric knot theory*.

There are several links to *physical knot theory* which comprises studying knots as physical objects, having a given length and thickness, and, more generally, any kind of knotted structure appearing in the sciences.

For instance, self-avoidance which is the central concept for modeling the above-mentioned geometric functionals has an impact in this context. Self-repelling forces are observed in the behaviour of protein foldings and the motion of knotted DNA structures. Knot energies are also considered in topological fluid dynamics.

The objective of this workshop is to present recent results from theory and applications and discuss future developments.

Acknowledgement: The workshop is supported by VARIOGEO (ERC Advanced Investigator Grant ERC-2010-AdG_20100224, Grant Agreement Number 267087).