RESEARCH

The research of the group inserts within the geometric topology of manifolds (or PL topology),  and focuses on crystallization theory, or gem theory,  which is a graph-theoretical representation method for compact PL-manifolds of arbitrary dimension, with or without boundary, making use of a particular class of edge-coloured graphs, dual to coloured (pseudo-) triangulations. 

One of the principal features of crystallization theory relies on the purely combinatorial nature of the representing objects, which makes them particularly suitable for computer manipulation (for details, see: DUKE III). 

Recent research deals with:

• relationships between crystallization theory and coloured tensor models in high dimensional quantum gravity (for example, see this poster)
• generation of catalogues of PL-manifolds for increasing values of the vertex number of the representing graphs, both in dimension three and four (for details, see: crystallization catalogues). 
• definition and/or computation of invariants for PL-manifolds, directly from the representing graphs, in dimension greater or equal to 3
• trisections of PL 4-manifolds - possibly with boundary - induced by colored graphs