Event Name

Fifth training course on symmetry and group theory; Sokendai Interdisciplinary Lecture

Start Date 6th Mar 2017
End Date 10th Mar 2017

Aim and target

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


The training course will span five full days, from 6 to 10 March, 2017. The program is essentially the same as that of the previous training courses.

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

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

Monday, 6 March

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

Tuesday, 7 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, 8 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, 9 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, 10 March

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

Coffee break will be served at 10:30 a.m. and 4 p.m. Lunch break will be 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 held at the seminar hall of the 4th building of KEK, Tsukuba campus.


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 and accommodation

Details are available at the this address.

Location Tsukuba
Contact Maki Okube
URL http://www.crystallography.fr/mathcryst/Tsukuba2017.php

Category Lectures | Training courses
Topics Mathematical and Theoretical Crystallography