11th Training course on symmetry and group theory

The training course on symmetry and group theory in Japan was launched in August 2014, immediately after the IUCr Congress in Montreal, on the occasion of the International Year of Crystallography. The motivation was to compensate for the lack for basic crystallography training in university curricula, which results in serious obstacles in daily crystallographic work when the investigator needs to interpret their results, navigate through the International Tables for Crystallography and perform all the tasks that a black box cannot do for them.

The training course is hosted at the High Energy Accelerator Organization site in Tsukuba and is offered free of charge to all students and scientists in Japan who need basic training in crystallographic symmetry. It is sponsored by the Crystallographic Society of Japan and the Institute of Materials Structure Science of the High Energy Accelerator Organization, and supported by a number of Japanese scientific societies and associations. It benefits from the precious help of Ms Yoshimi Takahashi, the dedicated secretary in charge of all the logistics and contact with participants.

The course spans five full days, with morning and afternoon lectures and exercises, and night sessions for questions and answers, discussion and support for the exercises. It is taught in its entirety by Professor Massimo Nespolo, from the Université de Lorraine (France). The unexpected success of the first course convinced the organizers to repeat it twice a year (March, August) until 2017, moving then to a once-a-year frequency when it became an official Interdisciplinary Lecture of the Graduate University for Advanced Studies (Sokendai), which entered as co-sponsor. This year it was held in July.

The programme of the training course starts from basic algebra to bring everybody to a common background, and goes through theory and practice of crystallographic point and space groups, with extensive exercises on the International Tables for Crystallography, crystallographic calculations, group–subgroup relations, normalizers, chirality, geometric derivation of reflection conditions, crystallographic orbits and symmetry aspects of phase transitions, with examples of derivative structures and construction of a structural model of low-symmetry polymorphs from high-symmetry polymorphs.

The course is taught entirely in Japanese. Because of the language difficulties met by foreign students willing to attend the lectures, an English version has been offered since 2019, but had to be interrupted because of the SARS-CoV-2 outbreak in 2020 and could only be restarted this year, after foreign students were again allowed to come and study in Japan. The Japanese course was only suspended in 2020; in 2021 it was offered in a hybrid form, before going back to on-site lectures in 2022.

An advanced course is offered periodically to those who have attended the basic course. The first advanced course was offered in 2016. The second advanced course, originally planned for 2020–2021, had to be postponed and was eventually realized this year, with a programme centred on groupoids and chromatic symmetry.

The 12th course is planned for July 2024, both in English and Japanese.