Geometric models

Discrete Structures

6th-24th January 2020

A structure (consisting of revolute joints linked by stiff bars, and modelled by a graph) is rigid if the configuration space of all realisations with the given bar lengths consists only of isometries of the original structure. In dimensions 1 and 2 the generic behaviour of such structures is completely characterised by matroidal properties of the underlying graph and hence is amenable to efficient algorithms. These algorithms are used frequently in applications (for example by biophysicists and structural engineers), and extending them to 3-dimensions would be of great applied and theoretical importance.

This problem was known certainly by the 1920s and no widely believed conjecture even exists despite the analogous 2-dimensional statement being completely solved in the 1970s. The aim of this focussed research group is to gather experts from combinatorics and geometry with researchers from neighbouring geometric and algebraic fields, in order to make a coordinated attack on the problem.

Organiser: Tony Nixon

This meeting is supported by a Heilbronn Institute for Mathematical Research focussed research grant.


The weeks of January 6-10 and 20-24 will mostly feature collaborative research on the topic in small groups. Each Friday there will be 1 or 2 talks in Lancaster's Rigidity Seminar.

The week of January 13-17 will feature a number of talks, mostly in the mornings, details of which can be found below. The afternoons will contain focussed group work and problem sessions. If you would like to enquire about the workshop please e-mail

  • Monday 13th
    • 9:30am-10:30am: Tibor Jordan
    • 11:15am-12:15am: Daniel Bernstein
    • 2pm: Problem session
  • Tuesday 14th
    • 9:30am-10:30am: Bill Jackson
    • 11:15am-12:15am: Meera Sitharam
    • 2pm: Problem session
  • Wednesday 15th
    • 9:30am-10:30am: Orit Raz
    • 11:15am-12:15am: Louis Theran
    • 2pm: Problem session
  • Thursday 16th
    • 9:30am-10:30am: Jim Cruickshank
    • 11:15am-12:15am: Georg Grasegger
    • 2pm: Problem session
  • Friday 17th
    • 9.30am-10.30am: Fatemeh Mohammadi


  • Daniel Bernstein (MIT)
  • Jim Cruickshank (Galway)
  • Daniel Garamvolgyi (Eotvos Lorand)
  • Georg Grasegger (RICAM/JKU Linz)
  • Hakan Guler (Kastamonu)
  • John Hewetson (Lancaster)
  • Bill Jackson (Queen Mary)
  • Tibor Jordan (Eotvos Lorand)
  • Oleg Karpenkov (Liverpool)
  • Lefteris Kastis (Lancaster)
  • Fatemeh Mohammadi (Bristol)
  • Tony Nixon (Lancaster)
  • Steve Power (Lancaster)
  • Orit Raz (Jerusalem)
  • Bernd Schulze (Lancaster)
  • Meera Sitharam (Florida)
  • Shinichi Tanigawa (Tokyo)
  • Louis Theran (St Andrews)
  • Joe Wall (Lancaster)

Travel information

The University provides information on travelling to Lancaster. The activities will take place in the Postgraduate Statistics Centre (marked PSC on the campus map) rooms B77 and B79 and the adjacent Fylde College (room B35).