Math. Phys. seminar at SISSA

[Emanuele Tuillier Illingworth]

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MATHEMATICAL PHYSICS SECTOR SEMINAR
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Prof. Peter Michor (Universitat Wien)

 Title:
 Curvature on diffeomorphism groups and nonlinear
 Grassmannians alias differentiable Chow varieties
 alias shape spaces.

 Abstract:
 For a Riemannian manifold M suitable Sobolev metrics
 on the space of vector fields induce right
 invariant weak Riemannian metrics on the group Diff(M)
 of all diffeomorphisms on $M$.
 This induces metrics on all spaces
 Emb(K,M) where K is a fixed compact manifold.
 Diff(M) as a subset of Emb(M,M) is also of this kind.
 As is the quotient Emb(K,M)/Diff(K).
 We study geodesic equations and curvature on all these spaces,
 in two different ways: With Arnold's curvature formula on Diff(M)
 and O'Neill's formula, or directly with `Mario's curvature formula',
 which is a new covariant way to compute curvature.
 This is joint work with David Mumford and Mario Micheli.

 Venue: Tuesday 16th June, 11:00, SISSA lecture room C




-- 
Dr. Emanuele Tuillier Illingworth
Secretary of Mathematical Physics and Elementary Particle sectors
phone (+39) 040 37 87 598
fax (+39) 040 37 87 466
SISSA
Via Beirut 2-4
Trieste, ITALY
emanuele.tuillierillingworth at sissa.it