Chirality and Symmetry Measures: some Open Problems

Programme: http://www.fields.utoronto.ca/programs/scientific/11-12/discretegeom/wksp_symmetry/International audienceA general framework to define symmetry and chirality measures is introduced. Then, we present a chirality measure (the chiral index) based on an extension of the Wasserstein metric to spaces of colored mixtures distributions. Connections with Procrustes methods and optimal RMS superpositions are outlined. The properties of the chiral index are presented, including its use as an asymetry coefficient of d-variate distributions. Relations with graph automorphisms groups and applications to chemistry are mentioned. Some maximally dissymetric or maximally chiral figures are presented. Several open problems are listed