MaThCryst satellite meeting: graph theory and modular structures

Organizers: Massimo Nespolo (University Lorraine, France)
                    Bernd Souvignier (Radboud University, Netherlands)
                    Berthold Stöger (TU Wien, Austria)
Date: 16th to 18th August 2019 (3 days)
Time: 9 a.m. – 6 p.m.


This workshop deals with mathematical and theoretical aspects of crystal structure descriptions beyond space group symmetry. The workshop will take place on two-and-a-half days.

The first day is devoted to the application of graph theory to crystal structure description. The combinatorial topology of a crystal structure is captured in a natural way by a graph with vertices representing the atoms (or functional groups) and edges representing the bonds between them. Using the periodicity of the crystal structure, this graph can be reduced to a finite labeled quotient graph with elements from the translation subgroup assigned to the edges. By reversing this construction, labeled quotient graphs provide a method to obtain hypothetical crystal structures.

The second day will treat the description of modular structures. These structures are built of distinct layers, rods or blocks. They are ubiquitous in all classes of compounds, from minerals to technological materials and pose challenging crystallographic problems, such as twinning, polytypism, disorder and systematic non-space group absences. Standard space group symmetry only considers global symmetry and does not reflect additional local symmetry of these structures. The full symmetry can be described using space groupoids. The order-disorder (OD) theory deals with special, though common, families of modular structures, where all members of a family are locally equivalent.

The morning of the third day is reserved for contributions by participants. Poster space will be provided.

The workshop will consist of introductory lectures and exercise sessions, where concrete examples will be worked out. Participants are expected to be familiar with the basic concepts of crystallography. No previous knowledge on graph theory or local symmetry is presupposed.

For travel grants see: TravelGrants.docx

For a detailed program and recent news, see