International School on Mathematical and Theoretical Crystallography

Montevideo, Uruguay, 29 November - 3 December 2010

The Commission on Mathematical and Theoretical Crystallography is strongly committed to promote education in all the fundamental aspects of crystallography that nowadays are overlooked in common University courses. This mission is accomplished through a series of meetings in a wide range of regions. In fall 2010 we organize a school in Montevideo, Uruguay, that continues our activity in the region after the previous school in Havana.

Program

• Affine spaces vs. vector spaces
• Mappings: affine and Euclidean; isometries
• Sets; homomorphisms, isomorphisms, automorphisms
• Symmetry operations as special case of isometries
• Introduction to group theory: abstract groups, subgroups, cosets

• Periodic structure of the crystalline matter
• Crystal lattice vs. crystal pattern and crystal structure
• Crystallographic calculations in direct space
• Symmetry directions in a lattice
• Unit cells: primitive cells, multiple cells, conventional cells in 2D and 3D
• Crystal families
• Symmetry groups and types of symmetry in direct space
  • morphological symmetry
  • symmetry of physical properties
  • symmetry of lattices
  • symmetry of the unit cell content
  • symmetry of crystallographic patterns
  • Hermann-Mauguin symbols for point groups
• Lattice systems
• Crystal systems
• Stereographic projection and the morphology of crystals
• Types of crystallographic point groups through the stereographic projection
• Symmetry operations with a glide component
• Space groups and types of space groups
• Exercises on the space group diagrams from Volume A of the International Tables for Crystallography
• Online tools for crystallography

• Fourier transforms and convolutions
• Crystallographic calculations in reciprocal space
• Diffraction symmetry: Laue classes, Friedel's law, resonant scattering
• Integral, zonal and serial reflection conditions and their use to determine the space-group type

• Magnetic symmetry - an extension of crystallographic symmetry.
• Magnetic groups - symmetry of spin arrangements
• Magnetic space group notations - Opechowski-Guccione; Shubnikov
• Black and white symmetry - relationship to magnetic symmetry
• Magnetic space group and magnetic subperiodic group tables

Language

The official language of the Schools is English. No simultaneous interpretation will be provided. However, local tutors will help the participants during the exercises.

Prerequisites

The participants are expected to know basic matrix algebra (how to multiply matrices and vectors, how to calculate determinant and trace of a matrix), fundamental electromagnetism (waves, diffraction) and basic chemistry. There will be a one day preparatory session, the day before the official start the school, for participants who need some help to comply with these pre-requisites.

Venue

Universidad de la Republica, Av. Gral. Flores 212, Casilla de Correos 1157, Montevideo, 11800, Uruguay

International Program Committee

Prof. Massimo Nespolo, Nancy-Université, Chair
Prof. Ernesto Estévez Rams, Universidad de la Habana, Cuba
Prof. Mois Ilia Aroyo, Universidad del Pays Basco, Bilbao, Spain
Dr. Leopoldo Suescun, Universidad de la Républica, Uruguay
Dr. Gustavo Echeverría , Universidad de La Plata, La Plata, Argentina
Dr. Eduardo Granado , UNICAMP, Campinas, SP, Brasil

Local Organizing Committee

Dr. Leopoldo Suescun, Chair [email protected]
Dr. Álvaro W. Mombrú [email protected]
Dr. Ricardo Faccio [email protected]
Dr. Helena Pardo [email protected]

Poster presentations

Participants are welcome to present posters, which will remain on display during the whole period of the school. Abstracts for the posters have to fit one page A4 size and should follow the templates available as OpenOffice writer, Rich-Text Format and Microsoft Word files. Abstract prepared with a Microsoft editor should be saved as Word2003 (.doc) and not Word2007 (.docx) format.

Abstracts should be submitted by email ; they will be collected in a PDF file and made available for download from this website after the school.

Registration, lodging, visa information

A separate website will be setup locally, with detailed information about registration fees and conditions, lodging, visa requirements.

Financial support

Limited financial support will be available for students and young scientists. Further details will be announced later.

Contact

Inquiries about the scientific program of the school should be sent to [email protected] .

For inquiries about lodging and logistic please contact [email protected]

The Organizers of the Montevideo 2010 MaThCryst school will observe the basic policy of non-discrimination and affirms 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 school no barriers will exist which would prevent the participation of bona fide scientists.