Geometric Rigidity Theory and Applications

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Geometric Rigidity Theory and Applications

 30 May - 03 Jun 2016

ICMS, 15 South College Street Edinburgh

Scientific Organiser

  • Robert Connelly, Cornell University
  • Bill Jackson, Queen Mary University of London
  • Stephen Power, University of Lancaster
  • Bernd Schulze, University of Lancaster

About:

A selection of photographs of this workshop are available here.

Geometric Rigidity Theory is concerned with the study of bar-joint frameworks and related constraint systems of geometric objects. The area can be traced back to classical work of Euler, Cauchy and Maxwell on the rigidity of polyhedra and skeletal frames. However in recent years the subject has become particularly active, drawing on diverse areas of mathematics and engaging with a growing range of applications. The activity is driven in part by the solution of some longstanding open problems, such as the so-called Molecular Conjecture, and the determination , of the generic nature of global rigidity, and by new connections with other mathematical areas, such as matrix completion theory or machine learning. Impetus in the area has also come from new themes such as constraint systems with point-group or crystallographic symmetries and constraint systems in general normed linear spaces. Both the generic combinatorial theory and symmetric geometric theories are  flourishing and in recent years the subject in general has increased its international visibility as an active research area.

The workshop brought together researchers to advance Geometric Rigidity through expositions of recent results, consultations between participants and through ensuing disseminations in research journals.

Speakers

  • Robert Connelly, Cornell University - Packing Equal Disks in a Square Torus

  • John Bowers, James Madison University - Non-Globally Rigid Inversive Distance Circle Packings

  • Ciprian Borcea, Rider University - Auxetic Periodic Designs

  • Brigitte Servatius, Worcester Polytechnic Institute - On the Size of 2D Rigid and Globally Rigid Subgraphs of of K-Valent Graphs

  • Offer Shai, Tel Aviv University - Rigidity Theory and Geometry in Engineering

  • Georg Nawratil, Vienna University of Technology - A Necessary Geometric Criterion for the Mobility of $n$-Pods

  • Franz Kiraly, University College London - Rigidity, Matroids and Matrix Completion

  • Anthony Nixon, Lancaster University - Global Rigidity of Frameworks on Surfaces

  • Meera Sitheram, University of Florida - Refutation of a Maximality Conjecture or a Combinatorial Characterization of 3D Rigidity

  • Viktoria Kazanitzky, Lancaster University - Sufficient Connectivity Conditions for Rigidity of Symmetric Frameworks

  • John Owen, Siemens UK - Independence and Smoothness for Non-Generic Frameworks

  • Hakan Guler, Queen Mary University of London - Rigidity of Body-Bar Frameworks

  • Hans-Peter Schröcker, University of Innsbruck - Kempe's Universality Theorem for Rational Space Curves

  • Shin-ichi Tanigawa, CWI & Kyoto University - Universal Rigidity, Singularity Degree, and Metric Polytopes of Signed Graphs

  • Bryan Chen, UMass Amherst - Topologically Polarized Periodic Frameworks and Applications to Toys and Origami

  • Gaiane Panina, St Petersburg State University - Discrete Morse Theory for Configuration Spaces of Flexible Polygons, or Solitaire Game on the Circle

  • Herman Servatius, Worcester Polytechnic Institute - Constrained Vector Configurations

  • Louis Theran, Aalto University - Generic Global and Universal Rigidity

  • Wai Yeung Lam, Technische Universität Berlin - Minimal Surfaces from Discrete Harmonic Functions

  • Vincenzo Vitelli, Leiden University - Topological Mechanical Metamaterials

  • Oleg Karpenkov, University of Liverpool - The Combinatorial Geometry of Stresses in Frameworks

  • Ileana Streinu, Smith College - Polyhedral Origami

  • James Cruickshank, National University of Ireland -  Block and Hole Graphs: More than One Block

  • Simon Guest, University of Cambridge - Counting Points and Lines with Symmetry

  • Tibor Jordan, Eötvös University - Robust Tensegrity Polygons

  • Katie Clinch, Queen Mary University - Symmetry-Forced Rigidity of Direction-Length Frameworks

  • Audrey St. John, Mount Holyoke College - Rigidity for Multi-Robot Formations

  • Leo Liberti, CNRS - Partial Reflection Groups and Distance Geometry of Henneberg Graphs

  • Hattie Serocold, Lancaster University - Rigidity of Frameworks with Coordinated Bars

  • Jessica Sidman, Mount Holyoke College - Special Positions of Bar-and-Joint Frameworks

  • Derek Kitson, Lancaster University - A Rigidity Theory for Matrices