Event Name

Fourth training course on symmetry and group theory

Start Date 7th Mar 2016
End Date 11th Mar 2016

Aim and target

This training course aims at providing a solid background in symmetry and group theory to students and scientists working on crystalline materials.


The training course spans five full days, from 7 to 11 March, 2016. The program is essentially the same as that of the previous training courses

Exercices proposed during the whole course are an integral part of the course: participants are requested to actively take part in solving the proposed exercises. Evening sessions will also be proposed for discussion, practicals, solution to the exercises, questions and answers.

Didactic material will be distributed during the lectures and also made available in electronic form.

Monday, 7 March

  • Matrix algebra
  • Abstract algebra and the notion of group
  • Introduction to crystallographic symmetry and lattices
  • Evening: welcome reception

Tuesday, 8 March

  • Morphological symmetry
  • Stereographic projection, with exercises
  • Crystallographic point groups and geometric crystal classes
  • Symmetry elements with a translational component (screw axes and glide planes)
  • Introduction to space groups: basic notions and the Hermann-Mauguin symbolism
  • Graphical construction of space groups
  • Evening (20:00-23:00): on-demand practicals, questions & answers optional session

Wednesday, 9 March

  • Practicals on the graphical construction of space groups
  • Metric tensor and applications
  • Matrix representation of symmetry operations
  • Change of axial settings and alternative settings of space groups
  • Evening (20:00-23:00): on-demand practicals, questions & answers optional session

Thursday, 10 March

  • Normalizers
  • Chirality
  • Wyckoff positions, wyckoff sets
  • Factor groups, symmorphic groups
  • Crystallographic orbits
  • Evening (20:00-23:00): on-demand practicals, questions & answers optional session

Friday, 11 March

  • Reciprocal lattice and systematic absences
  • Group-subgroup relations
  • Structure-substructure relations and applications to displacive phase transitions

Coffee breaks will be served at 10:30 a.m. and 4 p.m. Lunch break is from 12:30 p.m. to 2 p.m.


The official language of the training course is Japanese. No simultaneous interpretation will be provided.


The training course will be held at the KEK Tsukuba. Details will follow shortly.


Prof. Massimo Nespolo, Universit√© de Lorraine, France (on behalf of MaThCryst)

Local Organizing Committee

Dr Maki Okube, Tokyo Institute of Technology
Prof. Takashi Kamiyama, KEK
Prof. Noriyuki Igarashi, KEK


Registration will open early 2016 at the Japanese website .

Location Tsukuba
Contact Maki Okube
URL http://www.crystallography.fr/mathcryst/Tsukuba2016.php

Category Training courses
Topics Mathematical and Theoretical Crystallography