Detecting symmetry groups in crystallographic tilings

Speaker(s)

Bartosz Naskręcki

Affiliation

Uniwersytet im. Adama Mickiewicza

Language of the talk

English

Date

May 14, 2026, 4:15 p.m.

Room

room 5070

Seminar

Seminar "Mathematics and Physics of Complex Systems"

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In crystallography, identifying symmetry groups is crucial for understanding material properties and structures. Our research combines mathematical theory with machine learning to automate the detection of symmetry groups in crystallographic tilings.

By analyzing growth function coefficients derived from orphic diagrams, we develop a hierarchical classification approach that precisely identifies the 17 wallpaper groups in two-dimensional space. This interdisciplinary approach bridges pure mathematics with practical applications in crystallography and material science.

Crystallographic groups characterize the symmetry of periodic patterns in nature. The classification of these groups is well-established mathematically, but identifying them from physical data remains challenging. In two dimensions, 17 distinct wallpaper groups exist, each with unique combinations of translations, rotations, reflections, and glide reflections. Our work develops an AI-driven approach to classify these groups based on their growth characteristics rather than conventional geometric analysis.

Bibliography

https://journals.iucr.org/a/issues/2025/01/00/ae5152/index.html 

 

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