Colloque des sciences mathématiques du Québec

13 octobre 2006 de 16 h 00 à 18 h 00 (heure de Montréal/HNE) Sur place

Randomness, and its effects on Spectra

Colloque par Jean-Pierre Bourguignon (Inst. des Hautes Etudes Scientifiques (IHES))

It took several centuries to mathematicians to realize that a space can be intrinsically "curved". This lead to the discovery of non-Euclidean geometries. Bernhard Riemann introduced the mathematical tool that still now lies at the heart of our understanding of the concept of curvature, namely the "curvature tensor". Since it is a complicated object, both analytically and geometrically, many attempts have been made to cut it into pieces and to get at it from more geometrical points of view. Getting the curvature connected to more global properties of a space is still an active part of present day research in Geometry, as the spectacular developments concerning the PoincarŽ conjecture show. The purpose of the lecture is to try and give an overview of progress in our understanding of the curvature through a step by step analysis of the tools introduced in spite of the non-linear advancement of our knowledge.


CRM, UdeM, Pav. André-Aisenstadt, 2920, ch. de la Tour, Salle / Room 1140