January – March 2013 : Sergey Bobkov, a professor at University of Minnesota at Minneapolis, visited LAMA for two months from 7 january to 6 march 2013. He gave a series of three lectures devoted to ‘Entropy, central limit theorem, and related problems’. These lectures were related to his recent work on Berry-Essen bounds in the entropic central limit theorem. At the same time, he worked with N. Gozlan, C. Roberto (Université Paris 10) and P.-M. Samson on quantitative versions of the logarithmic Sobolev inequality for n-dimensional standard Gaussian measure. The deficit in the logarithmic Sobolev inequality is estimated by means of transport and information-theoretic distances. This work has been published in the Journal of Functional Analysis in 2014. In 2014, Bobkov, Gozlan, Roberto and Samson started a new collaboration on isoperimetric and Sobolev inequalities for convex domains of the Euclidean sphere. The Labex will support two one month stays of Bobkov in June 2015 and in 2016.