Arrival Day (14 June 2024-Friday) - afternoon
15:30 - 19:00 Arrival and registration of the participants.
19:00 - 20:30 Welcome Reception.
Pre-school Day (15 June 2024-Saturday): morning session (MN, MIA)
8.30 - 10:30 (MN) Revision 1 Crystallographic point groups.
Basic properties of groups (group axioms, order, multiplication tables, etc.). Subgroups, index, coset decompositions, Lagrange theorem. Concept of isomorphism and homomorphism. Group actions: conjugation and normalizers.
11:00 - 12:00 (MN) Revision 1 Crystallographic point groups (cont.)
Wyckoff positions for point groups. Overview of crystallographic point groups and their Hermann-Mauguin symbols.
12:00 - 13:00 (MIA) Revision 2 Matrix calculus applied to crystallography.
Isometries and crystallographic symmetry operations. Crystallographic point and space-group symmetry operations. Matrix-column presentation of symmetry operations. Symmetry elements: geometric elements and element sets.
Pre-school Day (15 June 2024-Saturday): afternoon session (MIA)
14:30 - 15:30 (MIA) Revision 2 Matrix calculus applied to crystallography (cont.)
15:30 - 16:30 (MIA) Revision 3: Representations of point groups
Representations of crystallographic groups: definition and basic properties. Irreducible and reducible representations.
17:00 - 19:00 (MIA) Revision 3: Representations of point groups (cont.)
Subduced and induced representations. Direct product representations. Database of Bilbao Crystallographic Server on point-group representations.
1st Day (16 June 2024-Sunday): morning session(MN)
08:30 - 09:00 Opening of the school.
09:00 - 10:30 (MN) Space-groups – general introduction:
Periodic structure of the crystalline matter: lattices and their basic properties. Structure of space-groups: point-groups of space-groups. Coset decomposition of the space-group with respect to its translation subgroup. Symmorphic and non-symmorphic space-groups.
Poster contributions-discussion during the coffee break.
11:00 - 12:00 (MN) Space-groups – general introduction (cont.) - Classification of space-groups.
12:00 – 13:00 (MN) Space-groups and their descriptions: Symbols of space-groups.
1st Day (16 June 2024-Sunday): afternoon session
14:30 - 16:30 (MN) Space groups and their descriptions (cont.):
Description of space-group symmetry operations. Space-group diagrams. General and special positions, sitesymmetry groups, crystallographic orbits.
Poster contributions-discussion during the coffee break.
17:00 - 19:00 (MIA) Representations of space groups:
Representations of the translation group. Symmetry in reciprocal space: Brillouin zones and wave-vector symmetry types. Irreducible representations of space groups and their construction. Subduced and direct-product representations of space groups. Brillouin-zone database of Bilbao Crystallographic Server. Basic computer tools for space-group representations.
1st Day (16 June 2024-Sunday): evening session (optional)
Discussions, questions and comments on the lecture and exercise material of the day.
2nd Day (17 June 2024-Monday): morning session(MN, MIA)
08:15 - 9:45 (MN) Transformations of the coordinate systems: change of origin and orientation. Conventional and non-conventional descriptions of space groups; ITA-settings.
09:45 - 10:30 (MIA) Group-subgroup relations between space groups:
Subgroups of space-groups: types of subgroups of space groups; Hermann theorem; maximal subgroups; series of isomorphic subgroups. Coset decomposition. Relations of Wyckoff positions for a group-subgroup pair. Supergroups of space-groups.
Poster contributions-discussion during the coffee break.
11:00 - 13:00 (MIA) Group-subgroup relations between space groups (cont.).
13:00 - 14:00 (MIA) Computer databases and access tools to crystallographic symmetry data for space-groups. Maximal subgroups data and related computer application in the Bilbao Crystallographic Server.
2nd Day (17 June 2024-Monday): afternoon session
14:30 - 19:00 Excursion in Shanghai.
19:30 - 22:00 Dinner in the town.
3rd Day (18 June 2024-Tuesday): morning session (MIA)
08:30 - 10:30 (MIA) Crystal-structure tools of the Bilbao Crystallographic Server:
Crystal-structure descriptions. Descriptions of crystal structures with respect to different ITA settings of the space groups (the program SETSTRU). Equivalent crystal-structure descriptions (the programs EQUIVSTRU and COMPSTRU). Crystal-structure descriptions compatible with symmetry reduction (the program TRANSTRU).
11:00 - 12:00 (MIA) Crystal-structure relationships. Family trees (Baernighausen trees) of crystal-structures: aristotype (basic) and hettotypes (derivative) structures (the program STRUCTURE RELATIONS).
12:00 - 13:00 (MIA) Structural pseudosymmetry. Pseudosymmetry search for new ferroics. Application in structural phase transitions (the program PSEUDO).
3rd Day (18 June 2024-Tuesday): afternoon session
14:30 - 16:30 (JMPM) Group-subgroup relations of space groups and their applications to phase transitions (SUBGROUPS, AMPLIMODES) - First part.
17:00 - 19:00 (JMPM) Group-subgroup relations of space groups and their applications to phase transitions (SUBGROUPS, AMPLIMODES) - Second part.
3rd Day (18 June 2024-Tuesday): evening session (optional)
Discussions, questions and comments on the lecture and exercise material of the day.
4th Day (19 June 2024 - Wednesday): morning session (JMPM)
08:30 - 10:30(JMPM)Magnetic symmetry. Magnetic point operations and point groups, connection to magnetic tensor properties. Magnetic space-groups and their presentation in D. Litvin’s tables. OG and BNS settings of type-IV magnetic space-groups.
11:00 - 13:00(JMPM) Representation analysis vs magnetic symmetry description of magnetic structures.
4th Day (19 June 2024-Wednesday): afternoon session (JMPM)
14:30 - 16:30(JMPM)Magnetic symmetry and its applications in the databases and tools of the Bilbao Crystallographic Server. Magnetic point and magnetic space-groups. General and special Wyckoff positions. Magnetic symmetry material tensors. Extinction rules for magnetic space-groups. Maximal magnetic space-groups for a given a propagation vector and resulting magnetic structural models.
17:00 - 19:00(JMPM)Database of magnetic structures on the Bilbao Crystallographic Server.
4th Day (19 June 2024-Wednesday): evening session (optional)
Discussions, questions and comments on the lecture and exercise material of the day.
5th Day (20 June 2024-Thursday): morning session(LZ)
8:30 - 10:30. (LZ) Chiral Phonons: definitions and theoretical description
11:00 -13:00 (LZ) Emergent phenomena with chiral phonons.
5th Day (20 June 2024-Thursday): afternoon session(MN, DA, BJC)
14:30 - 16:30(MN) Chirality: from molecules to crystal structures.
17:00 - 19:00 (DA) (on-line) Continuous symmetry and chirality measures: Principles and applications across the natural sciences.
19:00 - 21:00 (BJC) (on-line) A new symmetry-mode based descriptor of chirality. Applications to chiral organic-inorganic hybrid metal-halides.
21:00 - 23:00: Poster session (with buffet and drink)
6th Day (21 June 2024-Friday): morning session (SWC)
8:30 - 10:30 (SWC) Chirality and Kinetomagnetism.
11:00 -13:00 (SWC) Altermagnetism and Kinetomagnetism
6th Day (21 June 2024-Friday): afternoon session(GA, MC)
14:30 - 16:30 (GA) Chirality, Relativity and The Standard Model of Particle Physics.
17:00 - 18:00: (MC) How to get published and be read
18:00 - 18:30: Conclusion remarks. Final farewell and end of the school.