El viernes 21 de julio se realizará a las 15:30 un nuevo coloquio del Departamento de Matemática y Ciencia de la Computación. En esta oportunidad tendremos el agrado de escuchar a Hélène Eynard-Bontemps, de la Université Grenoble Alpes, cuya charla está titulada: From plane fields to foliations by surfaces on 3-manifolds.

Este evento se realizará de manera presencial en el auditorio del DMCC. Habrá galletitas y café para quienes asistan al evento.

Resumen: Foliations are beautiful and natural geometric objects. For example, the flow-lines of a non-vanishing vector field on a surface form a foliation of that surface by curves. In higher dimension also, one can come across foliations of manifolds by hypersurfaces, but they are much more difficult to construct in general. The point is that hyperplane fields (which generalize vector fields in higher dimension) rarely integrate to foliations, from dimension 3 on. However, William Thurston proved in the seventies that any hyperplane field can be deformed so as to become tangent to a foliation. In this talk, after a visual tour through the key notions and examples, I will present Thurston’s elegant argument in dimension 3 and, if time permits, examine to what extent it can help us understand the space of all foliations existing on a given 3-manifold.