International Union of Crystallography

MaThCryst forthcoming activities
First advanced training course on symmetry and group theory, August 2016, Tsukuba (Japan)
AIC School 2016, 711 September 2016, Rimini, (Italy)
Fifth MaThCryst School in Latin America, October 2016, Havana (Cuba)
Second Workshop on Mathematical Crystallography, May 2017, Manila (Philippines)
Shanghai International Crystallographic School, June 2017, Shanghai (China)
IUCr 2017 Satellite, September 2017, Rourkela, (India)
MaThCryst recent activities
International Scientific School 'Combined topological and DFT methods for prediction of new materials II', July 2016, Samara (Russia)
International School on Fundamental Crystallography with applications to Electron Crystallography, June  July 2016, Antwerp (Belgium)
SIAM conference on mathematical aspects of Material Science, May 2016, Philadelphia (USA)
Fourth training course on symmetry and group theory, March 2016, Tsukuba (Japan)
International Scientific School 'Combined topological and DFT methods for prediction of new materials', September 2015, Samara (Russia)
Third training course on symmetry and group theory, August 2015, Osaka, (Japan)
Second Balkan School on Fundamental Crystallography / Workshop on Magnetic Symmetry and its Application in Magnetic Structure Description, July 2015, Istanbul (Turkey)
More...
ECM26 XXVI European Crystallographic Meeting
MaThCryst Satellite Conference
Darmstadt, Germany, 27  29 August 2010
The XXVI European Crystallographic Meeting was held from 29 August to 2 September 2010 in Darmstadt, Germany.
The IUCr Commission on Mathematical and Theoretical Crystallography (MaThCryst) organised a Satellite Conference devoted to the analysis of crystal structure topology and mathematical interpretation of crystal structures.
Program
Lectures were completed with exercises distributed to the participants.
 Foundations of aperiodic structures made comprehensible (in cooperation with
the IUCr Commission on Aperiodic Crystals).
 Aperiodic crystals in the higherdimensional description. Incommensurately modulated structures (IMS), composite structures (CS) and quasiperiodic structures (QS)  similarities and dissimilarities
 Crystallography of Quasicrystals. Fibonacci sequence, Penrose tiling, octagonal tiling, random tilings  matching rules, symmetry, scaling. nD embedding, symmetry, structure factor. Description of real quasicrystal structures
 Some periodic crystal structures get simpler in higherdimensions.
 Introduction to Quaternions and Geometric Algebra and their applications in crystallography.
 Three dimensional Euclidean space
 Clifford's geometric algebra of R^{3}
 Subalgebra of quaternions
 Reflection in terms of plane normal vector
 Combination of reflections as geometric products
 Representations of point groups
 3+1 dimensional space time
 Time reversal as reflection at space hyperplane
 Magnetic point groups
 Explicit computations of symmetry transformations
 Homomorphism between unit quaternions and rotations
 Neighbouring grains of cubic polycrystals in coincidence misorientation
 Preferred grain boundaries and twinning of cubic crystals
 Triple junctions and quadruple nodes in cubic polycrystals
 Textures of arbitrary polycrystals described as distributions of unit quaternions
 Mathematics of minimal surfaces
 mean curvature
 variational definition of mean curvature
 some famous examples: helicoid, catenoid, Scherk, ...
 triply periodic examples: P, D, G, ...
 mathematical properties: maximum principle, stability
 mathematical tools to construct minimal surfaces: Plateau problem, Weierstrass data, perturbation methods
 significance of minimal versus constant mean curvature, Willmore/Helfrich etc.
 assumed periodicity versus self organizing structures
 minimal and cmc surfaces for given space groups: 1parameter families, bifurcations, distinct families
 classification problem for minimal surfaces w.r.t. a given space group
 genus of nets via quotient graphs
 minimal genus nets with good embeddings
 catenated netdual net pairs
 minimal surfaces as bicontinuous cellular patterns whose labyrinths are defined by these net pairs
 tricontinuous partitions and branched minima surfaces
 offsurface properties of minimal surfaces, including domain sizes and the problem of determining a skeletal (medial) representation from a given minimal surface
 noncubic minimal surfaces (in particular rhombohedral and tetragonal geometry) as transition surfaces between the cubic TPMS
Speakers
 Prof. Hans Grimmer, PSI Villigen (Switzerland)
 Prof. Eckhard Hitzer, Fukui, (Japan)
 Prof. Walter Steurer, ETH Zürich (Switzerland)
 Prof. Karsten GrosseBrauckmann, Darmstadt (Germany)
 Prof. Gerd SchroederTurk, Erlangen (Germany)
 Prof. Stephen Hyde, Canberra (Australia)
Exposition
A series of models illustrating the minimal surfaces was on display during the whole satellite conference.
Poster presentations
Participants presented posters, which remained on display during the three days of the satellite.
Schedule
 9:0010:30 Morning session I
 10:3011:00 Coffee break
 11:0012:30 Morning session II
 12:3014:00 Lunch break
 14:0015:30 Afternoon session I
 15:3016:00 Coffee break
 16:0018:00 Afternoon session II
Abstracts and didactic material
 Program and abstracts for the posters and for the contributed oral talks
 Quaternions and their application in crystallography (H. Grimmer)
 Skeletons in the Labyrint (G. SchröderTurk)
 Exercises on 3D periodic minimal surfaces and nets (S. Hyde)
 Aperiodic structures,.notions of .order and disorder (S. I. BenAbraham)
Participants
Name  Institution  

Stephen Hyde  Australian National University  
Joke Hadermann  University of Antwerp, Belgium  
Claudio Aguilar  Universiy Austral of Chile  
Massimo Nespolo  Nancy Université France  
Paolo Celani  Stoe&Cie GmbH, Germany  
Rachel Eloirdi  Institute for Transuranium Elements, Germany  
Christian Groçe  Georg August Universitât Gôttingen, Germany  
Karsten GrosseBrauckmann  Techniche Universitât Darmstadt, Germany  
Tim Gruene  GeorgAugustUniversitât, Germany  
Wilfrid E. Klee  BadenBaden, Germany  
Holger Kohlmann  Saarland University, Germany  
Sandrina Meis  RuhrUniversity Bochum, Germany  
Gerd SchroederTurk  Universitât ErlangenNuernberg, Germany  
Navdeep Sidhu  University of Goettingen, Germany  
Leonore Wiehl  GoetheUniversitât Frankfurt, Germany  
Hans Wondratschek  Karlsruher Institut fûr Technologie, Germany  
Shelomo BenAbraham  BenGurion University of the Negev, Israel  
Eckhard Hitzer  University of Fukui, Japan  
Takeo Matsumoto  Kanazawa University, Japan  
Ryoko Tomiyasu  High Energy Accelerator Research Organization, Japan  
Wilfried Wunderlich  Tokai University, Japan  
Bernd Souvignier  Radboud University, The Netherlands  
Leonid Pereyaslavets  Institut of Protein Research, RAS, Russia  
Mois Ilia Aroyo  University of the Basque Country, Spain  
Hans Grimmer  Paul Scherrer Institut, Switzerland  
Walter Steurer  ETH Zûrich, Switzerland  
Jonathan Coome  Durham University, UK 
Venue
The Satellite was held in the same venue as the ECM26 congress: the Darmstadtium congress centre.
Contact
Inquiries .
The Organizers of the ECM26 MaThCryst Satellite Conference observed the basic policy of nondiscrimination and affirmed 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 conference no barriers existed which would have prevented the participation of bona fide scientists.