Geometry and topology of liquid crystals and related ordered materials Niels Bohr Institute International PhD School (19-23 August 2013)

Summer school
Copenhagen, Danmark
This 5 ECTS point course will explore the geometry and topology of ordered cellular patterns such as foams, bicontinuous and polycontinuous forms and nets found in synthetic and biological materials, including:

  • mesoporous silicates
  • metal organic frameworks and coordination polymers
  • amphiphiles, lipids and star polyphiles
  • block copolymers including star miktoarm copolymers


    • Lectures will emphasise the fundamental structural aspects, with an introduction to the following concepts from modern geometry, crystallography and topology:

  • two-dimensional symmetries and orbifolds
  • graph theory and net embeddings
  • triply-periodic minimal surfaces and related polycontinuous patterns


    • No specialized mathematical knowledge is assumed, apart from some elementary familiarity with the shape of space, polyhedra and symmetry. The course will introduce students to unifying structural concepts in a range of ordered multi-phase hard/soft materials. We encourage students with theoretical or experimental backgrounds to attend.

    The course will familiarize students with open-source software for construction and characterization of structures from nets to surfaces. Hands-on tutorials will explore the concepts, via models and software.

    The course is free to attend, but all travel, accommodation and meals are at participants own expense. A limited number of participants will be chosen from the applicants.

    More detailed program and information will be posted here when available.

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