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International Union of Crystallography
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MaThCryst forthcoming activities
Twelth basic training course on symmetry and group theory, July 2024, Tsukuba (Japan)
Seventh MaThCryst School in Latin America, August 2024, Lima; (Peru)
MaThCryst recent activities
Eleventh basic and second advanced training course on symmetry and group theory, July 2023, Tsukuba (Japan)
Summer School, June 2023, Nancy (France)
Tenth training course on symmetry and group theory, August 2022, Tsukuba (Japan)
2022 Spring Festival Crystallographic School and Workshop on Crystal-field Applications February 2022, Berijing (China)
Crystallography Online: Workshop on the use and applications of the structural and magnetic tools of the Bilbao Crystallographic Server January 2022, Leioa (Spain)
Mathematics and Computer Science for Materials Innovation, September 2021, online
Ninth training course on symmetry and group theory, September 2021, Tsukuba (Japan)
2021 SIAM Conference on Mathematical Aspects of Materials Science, May 2021, Bilbao (Spain)
AMS Sectional Meeting, November 2019, Gainesville, FL (USA)
ECM32 Satellite, August 2019, Wien (Austria)
Eighth training course on symmetry and group theory, July 2019, Tsukuba (Japan)
Second Shanghai International Crystallographic School, July 2019, Shanghai (China)
Summer School, June 2019, Nancy (France)
Sixth MaThCryst School in Latin America, November 2018, Bogotà (Colombia)
More...
Shanghai International School on Crystallographic Groups and Representations, and Their Application in Magnetic-structure Descriptions and Topological-insulator Studies
International Center for Quantum and Molecular Structures
Shanghai University, Shanghai, China, 1-7 July 2019
SCIENTIFIC PROGRAM
Lectures:
Mois I. Aroyo (MIA) (Condensed Matter Physics Department, University of the Basque Country, UPV/EHU, Apto. 644, 48080 Bilbao, Spain)
B. Andrei Bernevig (AB) (Princeton University, Princeton, USA)
Barry Bradlyn (BB) (University of Illinois, Urbana?Champaign, USA)
Jennifer Cano (JC) (Stony Brook University and Flatiron Inst. Comput. Quantum Physics, USA)
Luis Elcoro (LE) (Condensed Matter Physics Department, University of the Basque Country, UPV/EHU, Apto. 644, 48080 Bilbao, Spain)
Massimo Nespolo (MN) (Université de Lorraine, Nancy, France)
Bernd Souivignier (BS) ((Radboud University, Nijmegen, The Netherlands)
Timetable:
Morning session (3h45'):
Lectures 8:15 - 10:15; 10:35 - 12:20
Coffee break: 10:15 - 10:35
Lunch: 12:20 - 13:45
Afternoon session (4h15'):
Lectures: 13:45 - 15:45; 16:15 - 18:30
Coffee break: 15:45 - 16:15
Dinner: 18:30 - 20:15
Evening session (optional): 20:30 - 21:30
1st Day (1 July 2019) morning session | |
08:15 - 08:30 | Opening of the school |
08:30 - 10:15 | (MIA) Crystallographic symmetry operations and their descriptions |
Crystallographic point and space-group symmetry operations. Matrix-column presentation of symmetry operations. Geometric interpretation of the matrix-column pairs of symmetry operations. Symmetry elements: geometric elements and element sets. | |
10:35 - 12:20 | (MN) Crystal pattern |
Crystal lattice vs. crystal pattern and crystal structure. 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. | |
1st Day (1 July 2019) afternoon session | |
13:45 - 14:45 | (MN) Crystallographic point groups |
Stereographic projection and the morphology of crystals. Hermann-Mauguin symbols for point groups. | |
14:45 - 15:45 | (BS) Crystallographic point groups (cont.) |
Basic properties of groups (group axioms, order, multiplication tables, etc.). Subgroups, index, coset decompositions, Lagrange theorem. | |
16:15 - 17:40 | (BS) Crystallographic point groups (cont.) |
Group actions: conjugation and normalizers. Wyckoff positions for point groups. Relations of Wyckoff positions for a group-subgroup pair. Supergroups of point groups. | |
17:40 - 18:30 | (MIA) Crystallographic point groups (cont.) |
Overview of crystallographic point groups. | |
Evening session (optional) | |
Discussions, questions and comments on the lecture and exercise material of the day | |
2nd Day (2 July 2019) morning session | |
08:15 - 10:15 | (BS) 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. | |
10:35 - 12:20 | (MN) Space groups and their descriptions |
Hermann-Mauguin symbols of space groups. Space-group diagrams. General and special positions, site-symmetry groups, crystallographic orbits. | |
2nd Day (2 July 2019) afternoon session | |
13:45 - 14:45 | (BS) Space groups and their descriptions (cont.): |
Symmorphic and non-symmorphic space groups. Classification of space groups. | |
14:45 - 15:45 | (MN) Space groups and their descriptions (cont.): |
Exercises on orthogonal projections of space groups 1. | |
16:15 - 18:30 | (MN) Space groups and their descriptions (cont.): |
Exercises on orthogonal projections of space groups 2. | |
Evening session (optional) | |
Discussions, questions and comments on the lecture and exercise material of the day | |
3rd Day (3 July 2019) morning session | |
08:15 - 10:15 | (MIA) Space groups and their description in International Tables for Crystallography |
Vol. A: Transformations of the coordinate systems: change of origin and orientation. Conventional and non-conventional descriptions of space groups; ITA-settings. | |
Hands-on session: Computer databases and access tools of the Bilbao Crystallographic Server(BCS) to crystallographic symmetry data for space: symmetry operations and their matrix-column presentation; geometric interpretation; general and special Wyckoff positions, site symmetry. | |
10:35 - 12:20 | (BS) General remarks on representations |
Representations of discrete groups. Equivalence of representations. Unitary representations. Invariant subspaces and reducibility. Theorem of orthogonality. Characters of representations and character tables. Subduced and direct-product representations. | |
3rd Day (3 July 2019) afternoon session | |
13:45 - 15: 45 | (BS) Representations of point groups |
Representations of Abelian groups: cyclic groups and direct products of cyclic groups. Character tables of representations of point groups. | |
16:15 - 18:30 | (MIA) Representations of groups: further developments |
Double point groups and their representations. Subduced and induced representations. Direct product representations. Representations of a group in terms of the representations of an invariant subgroup. | |
Evening session (optional) | |
Discussions, questions and comments on the lecture and exercise material of the day | |
4th Day (4 July 2019) morning session | |
08:15 - 10:15 | (MIA) Representations of space groups |
Representation of the translation group. Symmetry in reciprocal space: Brillouin zones and wave-vector symmetry types. Star of a representation. Little groups and small representations. Full-group representations of space groups | |
10:35 - 12:20 | (MIA) Representations of space groups (cont.) |
Double space groups and their representations. Subduced and direct-product representations of space groups. Compatibility relations and electronic energy bands. Site-symmetry approach and band representations. | |
13:45 - 14:45 | (MIA) Hands-on session with the computer tools of BCS for point- and space-group representations |
4th Day (4 July 2019) afternoon session | |
14:45 - 19:00 | Excursion in Shanghai |
19:00 - 22:00 | dinner in the town |
5th Day (5 July 2019) morning session | |
08:15 - 10:15 | (JC) Bloch's theorem and energy bands. |
Symmetry approach to tight-binding basis. Bands transform as space group irreps. Symmetry constraints. How to find little co-group irreps. | |
10:35 -12:20 | (BB) Berry phase and Zak phase. |
Polarization. Wannier functions. | |
5th Day (5 July 2019) afternoon session | |
13:45 - 15:45 | (BB, JC) Hands-on session: topological insulators with PythTB |
(Band structure, edge states, hybrid Wannier centers.) | |
16:15 - 18:30 | (AB) Topological insulators: general overview (strong/weak TI, TCI, Chern bands). |
Bulk-boundary correspondence. First generation topological materials. Automated materials search via topological quantum chemistry. | |
Poster session | |
18:30 - 21:00 | Poster session (with buffet and drink) ICQMS Building E 1/F |
6th Day (6 July 2019) morning session | |
08:15 - 10:15 | (JC) Band representations are not topological. |
Disconnected EBRs are topological. Quasi band representations. Symmetry indicators. | |
10:35 -12:20 | (BB) Absence of localized Wannier functions, Symmetry constraints on Berry phase and Wilson loops. |
Correspondence between Wilson loop spectrum and edge spectrum. | |
6th Day (6 July 2019) afternoon session | |
13:45 - 15:45 | (JC, BB, LE) Hands-on session with the computer tools of the BCS |
(BANDREP, Check Topological Materials) | |
16:15 - 17:00 | (JC, BB, LE) Hands-on session (cont.) |
17:00 - 18:30 | (AB) High-order topological insulators |
Evening session (optional) | |
Discussions, questions and comments on the lecture and exercise material of the day | |
7th Day (7 July 2019) morning session | |
08:15 - 10:15 | (MIA) Magnetic symmetry. |
Magnetic point operations and point groups, connection to magnetic tensor properties. Magnetic space groups. Types of magnetic groups. BNS and OG settings in type IV magnetic space groups. Wyckoff positions of magnetic space groups. | |
10:35 - 11:20 | (LE) Representations analysis vs. magnetic symmetry description of magnetic structures. Magnetic degrees of freedom. |
11:30 - 12:20 | (LE) Symmetry-based computational tools for magnetic crystallography in the Bilbao Crystallographic Server. |
Extinction rules for magnetic space groups (MAGNEXT). Possible magnetic groups for a given gray group and a propagation vector (k_SUBGROUPSMAG) and modelization/visualization ///(MAGMODELIZE,MVISUALIZE)// | |
7th Day (7 July 2019) afternoon session | |
13:45 - 16:15 | (LE) Hand-onl session: The Bilbao Crystallographic Server. |
MAXMAGN, k-SUBGROUPSMAG, MAGMODELIZE. Determine possible models for a given propagation vector. | |
16:45 - 17:30 | (LE) Database of magnetic structures on the Bilbao Crystallographic Server. |
18:00 - 18:30 | Final farewell remarks: end of the school |
Registration and accommodation
All the details are available at the local website.
Special issue announcement
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A special issue of Crystal Research and Technology has published a special issue containing a collection of papers submitted on the occasion of MaThCryst 2019 Summer events. |
The Organizers of the Shanghai Crystallographic School have observed 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 barrier existed which would have prevented the participation of bona fide scientists.