The Erwin Schroedinger Institute for Mathematical Physics

Workshop: Rigidity and Flexibility of Geometric Structures

The mathematical study of the rigidity and flexibility of discrete structures can be traced back to classical work of Euler, Cauchy and Maxwell on the rigidity of polyhedra and skeletal frames. The subject has increased its international visibility as an active research area over the last 5 years, 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 and by connections with nearby mathematical areas, such as distance geometry and topology.

Both theoretical (combinatorics, algorithms, discrete and algebraic geometry) and applied (materials geometry, robot kinematics, symbolic computation) aspects of rigidity and flexibility are flourishing and influencing each other.

In simple terms, the geometric and combinatorial rigidity community focuses on multiple approaches for detecting whether an input set of polynomial equations representing a geometric constraint system (a) has a solution (independence), (b) has continuous paths of solutions (flexibility), (c) has locally isolated solutions (rigidity), or (d) has exactly one solution up to a space of ``trivial'' transformations in the chosen geometry (global rigidity).

The workshop will focus on the following key topics:

  • Flexibility of structures, linkages and their configuration spaces;
  • Combinatorial rigidity, algorithms and enumeration problems;
  • Global rigidity, graph realisations and applications.
Organising committee:

Georg Nawratil (TU Vienna), Anthony Nixon (Lancaster), Josef Schicho (JKU Linz) and Brigitte Servatius (WPI).

The workshop will feature a selection of keynote speakers and a number of shorter talks. On the Monday morning there will be two introductory lectures for those new to the subject.

Introductory lectures:

  • Bill Jackson (Queen Mary)
  • Hellmuth Stachel (TU Vienna)
  • Keynote presentations:

  • Matteo Gallet (RICAM)
  • Ivan Izmestiev (Fribourg)
  • Oleg Karpenkov (Liverpool)
  • Leo Liberti (CNRS)
  • Gaiane Panina (St Petersburg)
  • Meera Sitharam (Florida)
  • Louis Theran (St Andrews)