2009 DG-MP-PDE Seminar - 05

  • Date: 07/29/2009
Lecturer(s):

Christian Duval (Centre de Physique Theorique, Universite d'Aix-Marseille II, Luminy)

 

Location: 

University of British Columbia

Topic: 

On the Euclidean, affine, and projective invariants of the supercircle, and their associated cocycles

Description: 

Starting from the standard contact structure of the supercircle, S^{1|1}, one considers the subgroups E(1|1), Aff(1|1), and SpO(2|1) of the group, K(1), of its contactomorphisms that respectively define its Euclidean, affine, and projective geometries. The notion of p|q-transitivity allows one to systematically construct the characteristic invariants of each geometry, in particular the super cross-ratio. One deduces the nontrivial associated 1-cocycles of K(1), e.g., the superschwarzian. The case of the supercircle S^{1|2} is also studied. The aim of this talk is to present in a synthetic fashion these geometric objects which are somewhat scattered in the literature. This is joint work with J.-P. Michel.

Abstracts / Downloads / Reports: 
Sem-UBC-29-07-09.pdf
Schedule: 

3:00pm, WMAX 216

Sponsor: 

pims