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International Union of Crystallography
Commission on Mathematical and Theoretical Crystallography

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Training course on symmetry and group theory
Sokendai Interdisciplinary Lecture

Sponsors: The Crystallographic Society of Japan, Institute of Materials Structure Science of the High Energy Accelerator Organization
Co-sponsors: Sokendai (the Graduate University for Advanced Studies)
Supporters: The Japanese Society for Neutron Science, The Japanese Society for Synchrotron Radiation Research, The Chemical Society of Japan, The Japan Society of Applied Physics, The Iron and Stell Institute of Japan, The Physical Society of Japan, The Japanese Society of Microscopy, The Japan Institute of Metals and Materials, The Japan Association of Mineralogical Sciences, The Japan Society for Analytical Chemistry

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Aim and target

The training course is normally held biannually (March and August) and aims at providing a solid background in symmetry and group theory to students and scientists working on crystalline materials. It is divided in two branches:

  1. Basic course: open to everybody, no pre-requisite apart from basic matrix algebra:
  2. Advanced course: open to former participants of the basic course.

Both courses usually span five full days. Exercises 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 proposed for discussion, practicals, solution to the exercises, questions & answers. Didactic material is distributed before and during the lectures and also made available in electronic form.


Basic course

Advanced course

The program of the advanced course is tuned to fit the interest of the participants and is annoucend before the registration opens.

Schedule of the courses

Basic course

Advanced course


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

Sokendai Interdisciplinary Lecture

From the fifth basic course, this training course has become part of the education provided by Sokendai, the Graduate University for Advanced Studies: University students can get credits through this university for attending the training course.

Lecture notes

The content of the lectures of the basic course is now partly being published in a series of didactic articles in the Journal of the Crystallographic Society of Japan. The articles published so far are available from the J-Stage webiste at the following addresses:


The training course is normally held at KEK, Tsukuba campus. Occasionally, alternative venues are considered, depending on the availability of the facilities and local organizers. The third basic was held at the Institute for Protein Research, Osaka University.


Prof. Massimo Nespolo, Université de Lorraine, France (on behalf of MaThCryst)

Local Organizing Committee in Tsukuba

Prof. Takashi Kamiyama, KEK (Chair)
Prof. Noriyuki Igarashi, KEK
Ms. Yoshimi Takahashi, KEK (Secretary)


The organizers of the training course are deeply indebted to Dr. Maki Okube (SuperOx Japan LLC and Tokyo Institute of Technology), initiator for the course, for her strong involvement and continuous support.

Further information

Details are available at the Japanese web site.

The Organizers of the trainng course 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 exist which would prevent the participation of bona fide scientists.

Last updated: 29th July 2023
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