Event

Talk
Ricci flow, entropies and the averaging of cosmological spacetimes
Mauro Carfora
23 Nov 2006, 9:00

I will discuss Ricci flow deformation of cosmological Initial data sets. This is one of the oldest application of the Ricci flow, devised in an attempt to formalize G.F.R. Ellis' fitting problem and cosmological averaging program. Initial data set deformation generate curvature back-reaction effects in the cosmological modelling of the curvature of the physical space. They have recently drawn attention in the controversial issue as to what is the origin of the acceleration of the Universe. Regardless of their actual role in physical cosmology, I will argue that Ricci flow deformations of the initial data sets for Einstein equations provide a number of challenging mathematical problems. We show that Perelman's extension of the Ricci flow sheds new light on such an issue, in particular we analyze the role that entropy-like quantities may have in controlling the deformation procedure.

Notes (PDF): http://www.aei.mpg.de/~olito/WS/Talks/Carfora.ppt