Event Name

Third training course on symmetry and group theory

Start Date 3rd Aug 2015
End Date 7th Aug 2015

Third training course on symmetry and group theory

Osaka, Japan, 3-7 August 2015

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 participants are expected to know basic matrix algebra (how to multiply matrices and vectors, how calculate determinant and trace of a matrix: however, the first session of the training course is devoted to revise these notions), fundamental electromagnetism (waves, diffraction) and basic chemistry.


The training course will span five full days, from 3 to 7 August, 2015.

Exercices proposed during the whole course are 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 & answers.

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

Monday, 3 August

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

Tuesday, 4 August

  • 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, 5 August

  • 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, 6 August

  • 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, 7 August

  • 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. Dinner from 6 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 Institute for Protein Research, Osaka University, seminar room at the first floor.


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, Tsukuba
Prof. Noriyuki Igarashi, KEK, Tsukuba


Prof. Genji Kurisu, IPR, Osaka

Lodging, financial support and registration

Participation is free of charge. Details about lodging, application for financial support and registration form are available at the Japanese website .

The Organizers of the trainng course will observe the basic policy of non-discrimination and affirm the right and freedom of scientists to associate in international scientific activity without regard to such factors as citizenship, religion, creed, political stance, ethnic origin, race, colour, language, age or sex, in accordance with the Statutes of the International Council for Science. At this course no barriers existe which would prevent the participation of bona fide scientists.

Location Osaka
Contact Prof. Genji Kurisu, IPR, Osaka
URL http://www.crystallography.fr/mathcryst/Osaka2015.php

Category Training courses
Topics Mathematical and Theoretical Crystallography