Summer Schools on Mathematical Crystallography

Nancy, France, 21 June - 2 July 2010

Program The two schools will run one after the other, with a pre-school optional day where the basic concepts necessary to attend the schools will be presented. Participants to the pre-school day will be required doing some concrete exercises allowing them to get familiar with the bases that are assumed understood during the school. The weekend between the two schools will be devoted to presenting additional concepts that are pre-requisite to attend the second school. Participants familiar with these topics will be given the alternative of some optional excursions (not included in the registration fees). Pre-school day 21 June: Introduction to crystal symmetry; space groups, Hermann-Mauguin symbols, exercises on the International Tables for Crystallography Topological Crystal Chemistry: Theory and Practice The first school will run on four days, from 22 to 25 June * Crystal nets as graphs. Introduction to graph theory. * Deconstruction of crystal structures. * Tilings for nets. Dual structures, transitivity. * Taxonomy of nets. Regular, Semiregular etc. * Knots and Entanglements in crystals. * Use of Topos, RCSR and EPINET databases. Weekend intermission 26-27 June: subgroups of space groups; matrix algebra applied to crystallographic problems. Irreducible representations of space groups The second school will run on five days, from 28 June 2 July * Basic facts on crystallographic groups * Basic facts on subgroups of space groups * Basic facts on representation theory and irreducible representations (irreps) of crystallographic groups (point groups) * Induction procedure for the derivation of irreps * Application of the induction procedure for the derivation of the point group irreps * Irreps of space groups * Group-subgroup relations in phase transition problems * Phase transitions-Landau theory approach * Phonons