Van der Waals-Zeeman Colloquium
Thursday, 9 December 2010, 16:00 (SPA, G2.10)
From Soft Matter to Dark Matter: the Statistical Physics of Lensing
Prof. Vincenzo Vitelli
When soft matter orders on a curved surface, intriguing patterns of elastic distortions arise from the competition between bending and compression. Often, these phenomena can be understood by combining elasticity with a simple geometrical principle: curvature causes geodesics and elastic energy to focus, in analogy to the focusing of light rays by a lens. In the first part, of this talk I will present a theory of curved space crystallography built around this principle and discuss its predictions in the light of recent experimental studies of colloidal monolayers confined on curved capillary bridges. Elastic focusing has a close higher-dimensional analogue in gravitational lensing. The images of distant galaxies undergo shear distortions that display coherent patterns from which the clustering of dark matter can be inferred. I will present a geometric view of this process that relates the distribution of topological defects in the cosmic shear to the curvature of an imaginary surface prescribed by the lensing potential. This allows one to obtain crucial information about the correlation function of mass fluctuations from the abundance of defects in shear maps. I will conclude with a discussion of topological tests of non-gaussianities in this type of cosmological signals.