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conference
26/03/2014 28/03/2014

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).

Speakers

Dorothy Buck

Imperial College, United Kingdom

Elizabeth Denne

Washington & Lee University, USA

Thomas El Khatib

Technische Universität Berlin, Germany

Aya Ishizeki

Saitama University, Japan

Martin Meurer

RWTH Aachen, Germany

Takeyuki Nagasawa

Saitama University, Japan

Chiara Oberti

University of Milano-Bicocca, Italy

Sylwester Przybył

Poznań University of Technology, Poland

Renzo Ricca

Università di Milano, Italy

Sebastian Scholtes

RWTH Aachen, Germany

John Sullivan

TU Berlin, Germany

Marta Szumańska

University of Warsaw, Poland

Alexander Volkmann

Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Germany

Heiko von der Mosel

RWTH Aachen, Germany

Program

Mar 26, 2014
08:00 - 08:50
08:50 - 09:00
09:00 - 10:00 Dorothy Buck (Imperial College, London, United Kingdom)
Knotted DNA: Mathematical Models and Biological Consequences
10:00 - 10:30
10:30 - 11:30 Renzo Ricca (Università di Milano, Milano, Italy)
Relaxation of magnetic knots to braids and groundstate energy minima
11:30 - 12:00
12:00 - 12:30 Chiara Oberti (University of Milano-Bicocca, Milano, Italy)
Energy and self-linking of magnetic torus knots
12:30 - 14:00
14:00 - 15:00 Michael Struwe (ETH Zurich, Switzerland)
15:00 - 15:30
15:30 - 16:30 Sylwester Przybył (Poznań University of Technology, Poznań, Poland)
The shape and curvature of the twisted clasp
16:30 - 17:00
Mar 27, 2014
09:00 - 10:00 Heiko von der Mosel (RWTH Aachen, Aachen, Germany)
The elastic trefoil is the twice covered circle
10:00 - 10:30
10:30 - 11:00 Aya Ishizeki (Saitama University, Saitama, Japan), T. Nagasawa
Decomposition of the Möbius energy I: A decomposition theorem and Möbius invariance
11:00 - 11:30
11:30 - 12:30 Takeyuki Nagasawa (Saitama University, Saitama, Japan), A. Ishizeki
Decomposition of the Möbius energy II: The first and second variational formulas
12:30 - 14:00
14:00 - 14:30 Alexander Volkmann (Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Potsdam, Germany)
Sharp geometric inequalities for curves and surfaces with boundaries
14:30 - 15:00
15:00 - 15:30 Sebastian Scholtes (RWTH Aachen, Aachen, Germany)
Discrete curvature energies
15:30 - 16:00
16:00 - 17:00
19:00 - 23:00
Mar 28, 2014
09:00 - 10:00 John Sullivan (TU Berlin, Berlin, Germany)
Supercoiled helices: strut-free critical curves for ropelength
10:00 - 10:30
10:30 - 11:30 Elizabeth Denne (Washington & Lee University, Lexington, USA), John Sullivan and Nancy Wrinkle
Flat ribbons for link diagrams
11:30 - 12:00
12:00 - 12:30 Thomas El Khatib (Technische Universität Berlin, Berlin, Germany)
Thickening Dubins Curves
12:30 - 14:00
14:00 - 14:30 Martin Meurer (RWTH Aachen, Aachen, Germany)
Which kind of integral Menger-type curvature is suitable for a generalization of L\'{e}ger's theorem?
14:30 - 15:00
15:00 - 15:50 Marta Szumańska (University of Warsaw, Warsaw, Poland)
Applications of t-energies to analysis of vortex sheets
16:00 - 16:30

Participants

Pierre Baudot

Max Planck Institute for Mathematics in the Sciences, Germany

Simon Blatt

Universität Karlsruhe, Germany

Dorothy Buck

Imperial College, United Kingdom

Elizabeth Denne

Washington & Lee University, USA

Thomas El Khatib

Technische Universität Berlin, Germany

Nadine Große

Universität Leipzig, Germany

Aya Ishizeki

Saitama University, Japan

Nai-Huan Jing

South China Univ of Tech, China

Enno Keßler

Max Planck Institute for Mathematics in the Sciences, Germany

Jan Knappmann

RWTH University Aachen, Germany

Sebastian Melzer

TU Dresden, Germany

Martin Meurer

RWTH Aachen, Germany

Takeyuki Nagasawa

Saitama University, Japan

Chiara Oberti

University of Milano-Bicocca, Italy

Sylwester Przybył

Poznań University of Technology, Poland

Philipp Reiter

Universität Duisburg-Essen, Germany

Renzo Ricca

Università di Milano, Italy

Armin Schikorra

Max Planck Institute for Mathematics in the Sciences, Germany

Sebastian Scholtes

RWTH Aachen, Germany

John Sullivan

TU Berlin, Germany

Marta Szumańska

University of Warsaw, Poland

Jürgen Tolksdorf

Max Planck Institute for Mathematics in the Sciences, Germany

Tat Dat Tran

Max Planck Institute for Mathematics in the Sciences, Germany

Alexander Volkmann

Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Germany

Heiko von der Mosel

RWTH Aachen, Germany

Ruijun Wu

Max Planck Institute for Mathematics in the Sciences, Germany

Chao Xia

Max Planck Institute for Mathematics in the Sciences, Germany

Miaomiao Zhu

Max Planck Institute for Mathematics in the Sciences, Germany

Scientific Organizers

Simon Blatt

Karlsruher Institut für Technologie

Philipp Reiter

Universität Duisburg-Essen

Armin Schikorra

Max-Planck-Institut für Mathematik in den Naturwissenschaften

Administrative Contact

Antje Vandenberg

Max-Planck-Institut für Mathematik in den Naturwissenschaften Contact via Mail