Event Name Second Training course on symmetry and group theory
Start Date 9th Mar 2015
End Date 13th Mar 2015
Duration 5 days

In the framework of the International Year of Crystallography, the IUCr Commission on Mathematical and Theoretical Crystallography organizes a second training course on "symmetry and group theory" at Tsukuba, Japan, on 9 to 13 March 2015.


The participants are expected to know basic matrix algebra (how to multiply matrices and vectors, how calculate determinant and trace of a matrix: however, an optional half-day is devoted to revise these notions), fundamental electromagnetism (waves, diffraction) and basic chemistry.


The training course will span five full days, from 9 to 13 March, 2015. Monday morning (March 9) is optional for those needing to revise general concepts about matrix algebra and abstract algebra (general introduction to group theory). Exercices proposed during the whole course are integral part of the course: participants are expected to actively participate and solve the proposed exercises.

Monday, 9 March

  • Morning: optional session on matrix and abstract algebra
  • Afternoon: introduction to crystallographic symmetry and lattices

Tuesday, 10 March 15

  • Morphological symmetry
  • Stereographic projection, with exercises
  • Crystallographic point groups and geometric crystal classes
  • Matrix representation of point group operations
  • Symmetry elements with a translational component (screw axes and glide planes)

Wednesday, 11 March

  • Introduction to space groups
  • Graphical construction of space groups
  • Metric tensor and applications
  • Change of axial settings and alternative settings of space groups

Thursday, 12 March

  • Reciprocal lattice and systematic absences
  • Matrix representation of space group operations
  • Crystallographic orbits

Friday, 13 March

  • 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 be held at the KEK 4th bulding, seminar room


Prof. Massimo Nespolo, Université 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

Japanese website

A Japanese website is available at this address.

Location Tsukuba
Contact Maki Okube
URL http://www.crystallography.fr/mathcryst/Tsukuba2015.php
Category schools and workshops