Benoît Daniel, from the University of Lorraine, will give the geometry seminar on 20th October, at 2pm in O8.08, 8th floor of building NO. His title is *Minimal isometric immersions into $latex S^2 \times \mathbf{R}$ and $latex H^2 \times \mathbf{R}$.* His abstract follows.

A classical result in submanifold theory is that any simply connected minimal surface in Euclidean space R^3 belongs to a one-parameter family of minimal surfaces that are (intrinsically) isometric to it; this family is called the associate family. Conversely, two isometric minimal surfaces are associate. We will study a generalisation of this result when the ambient manifold is a Riemannian product $latex S^2\times\mathbf{R}$ or $latex H^2\times\mathbf{R}$ (where $latex S^2$ and $latex H^2$ respectively denote the constant curvature sphere and the hyperbolic plane). For this purpose we will make a connection between this problem and the study of a system of two partial differential equations.