The Conference intends to discuss emerging tendencies in research within the geometric topology of manifolds in dimension three and four, with a particular attention to different combinatorial tools for studying PL-manifolds (knots and braids, branched coverings, framed links, Heegaard diagrams, colored graphs, trisections…), as well as to the interconnections with other disciplines.
A specific focus will be placed on the application of the representation theory by edge-colored graphs (gem theory or crystallization theory) to the study of random tensors, employed in theoretical physics as an approach to quantum gravity in arbitrary dimension.
Application-oriented topics are discussed in the second part of the conference with a more educational perspective.
In particular, contributions will be included on:
- Geometrical aspects in classical and contemporary art:
- symmetry, perspective, representation of non-Euclidean spaces
- relevant examples in Reggio Emilia (pavement of the Tempio della Ghiara, proportions of the cloisters of San Pietro)
- the great “artists-mathematicians” (Leonardo da Vinci, Piero della Francesca, M. C. Escher)
- Connection between Geometry and Astronomy:
- surface covering and radar scan of celestial bodies, and the discovery of liquid water on Mars
- outreach activities (REA – Reggio Emilia Astronomia)
- The contribution of the great scientists from Reggio to modern Geometry (e.g., Giuseppe Sforza and the volume of the hyperbolic tetrahedron)
- Applications of tessellations to the engineering of metamaterials.