Résumé : A two-dimensional cluster, growing by aggregation of a sequence of particles, may be encoded as a composition of conformal maps. This offers a means to formulate and analyse models for planar random growth. I will focus on scaling limits in the case where there are many small particles, first for the case where the conformal maps are chosen to be independent, and then for a variant model which takes the fluctuations of the process towards a critical point, which is a limit of stability.
Joint work with Vittoria Silvestri and Amanda Turner.

Résumé : In this talk I will present a new proof of the partial regularity of optimal transport maps. As opposed to the previous proof of Figalli and Kim which was using Caffarelli’s approach to regularity of solutions of Monge-Ampere equations via maximum principles arguments, our proof is variational in nature. By using the fluid-dynamic formulation of optimal transportation (which usually goes by the name of Benamou-Brenier formulation) we prove that at every scale, the optimal transport map is close to the gradient of an harmonic function. This allows us to set up a Campanato iteration scheme to obtain the desired regularity. This is joint work with F. Otto.

Lieu : Amphi Schwartz

Résumé : In the first part of the talk, we will introduce spatial Gaussian processes.
Spatial Gaussian processes are widely studied from a statistical point of view, and have found applications in many fields, including geostatistics, climate science and computer experiments. Exact inference can be conducted for Gaussian processes, thanks to the Gaussian conditioning theorem. Furthermore, covariance parameters can be estimated, for instance by Maximum Likelihood.
In the second part of the talk, we will introduce a class of iterative sampling strategies for Gaussian processes, called ’stepwise uncertainty reduction’ (SUR). We will give examples of SUR strategies which are widely applied to computer experiments, for instance for optimization or detection of failure domains. We will provide a general consistency result for SUR strategies, together with applications to the most standard examples.

Lieu : Salle 106 1R1