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Description
Mosaic patterns and tilings are ubiquitous in nature, appearing in systems ranging from cellular tissues and geological formations to biological shells and foams. Traditionally, these structures have been modeled using polyhedral tilings composed of flat faces, straight edges, and sharp corners. However, careful observation reveals that many natural tilings deviate significantly from this paradigm: their boundaries are curved with smooth interfaces. This realisation has motivated the introduction of a new class of shapes known as soft cells, which arise as smooth deformations of standard tilings. Such cells are found in the geometry of metal and liquid foam as well as in many micro-structures modelled by triply periodic minimal surfaces. In this talk, I will explain the mathematics and physics of tilings, hard and soft, describe their construction and classification, and illustrate how they provide a more accurate geometric description of patterns found in biology, architecture, engineering, in the deepest sea and even in space.
About the speaker:
Alain Goriely obtained his PhD from the Université libre de Bruxelles in 1994 before joining the University of Arizona where he eventually became a Professor. In 2010, he moved to Oxford to take up the inaugural chair of Mathematical Modelling and to become Director of the Oxford Centre for Collaborative Applied Mathematics (OCCAM). He is also co-director of the International Brain and Mechanics Lab and a fellow of the Royal Society since 2022 and the recipient of several awards, including the David Crighton Medal in 2025. He works on a wide range of topics in applied mathematics, from the modeling of brain and cancer to the development of new photovoltaic devices and batteries. His research also has more theoretical aspects, ranging from the foundations of mechanics to the dynamics of curves, knots and rods.