David Mumford Professor Emérito da Universidade de Brown

26 de março
Auditório Ricardo Mañé às 17 horas
Título: Geodesic warping of Euclidean space, its dynamics, curvature and applications

Abstract: Since Durer, warping images has been studied. I will describe an elementary approach to warping in any dimension based on Sobolev metrics, landmark points and differential geometry. The talk will link this work with Arnold's geometric theory of Euler's equation and show applications to medical imaging and an ancient Chinese map.

28 de março
Auditório Ricardo Mañé às 17 horas
Título: Life in Infinite dimensions -- a tour of its widely varying offerings

Abstract: Riemann proposed a geometry of infinite dimensional manifolds long ago in his Habilitation talk. What I think he did not anticipate is that depending on the metric, these spaces can be so diverse. We can have so much positive curvature that conjugate points are dense on geodesics. We can have homogeneous spaces with negative curvature but finite Ricci curvature. And associated to hydrodynamics, we can have a complex curvature picture that still hasn't been untangled. We will give an illustrated tour.

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