Cours/Séminaire
Notice
Langue :
Anglais
Crédits
Fanny Bastien (Réalisation), Joseph H. G. Fu (Intervention)
Conditions d'utilisation
CC BY-NC-ND 4.0
DOI : 10.60527/dja6-xw44
Citer cette ressource :
Joseph H. G. Fu. I_Fourier. (2015, 22 juin). Joseph Fu - Integral geometric regularity (Part 1) , in 2015. [Vidéo]. Canal-U. https://doi.org/10.60527/dja6-xw44. (Consultée le 19 mars 2024)

Joseph Fu - Integral geometric regularity (Part 1)

Réalisation : 22 juin 2015 - Mise en ligne : 1 juin 2016
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Descriptif

In the original form given by Blaschke in the 1930s, the famous Principal Kinematic Formula expresses the Euler characteristic of the intersection of two sufficiently regular objects in euclidean space, integrated over the space of all possible relative positions, in terms of geometric invariants associated to each of them individually. It is natural to wonder about the precise regularity needed  for this to work. The question turns on the existence of the normal cycle  of such an object A, i.e. an integral current that stands in for its manifolds of unit normals if A is too irregular for the latter to exist in a literal sense. Despite significant recent progress, a comprehensive understanding of this construction remains maddeningly elusive. In these lectures we will discuss both of these aspects.

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