Life in Infinite dimensions -- a tour of its widely varying offerings.
Mumford, David, 1937-
Life in Infinite dimensions -- a tour of its widely varying offerings. - Rio de Janeiro: IMPA, 2012. - video online
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.
Matematica.
Life in Infinite dimensions -- a tour of its widely varying offerings. - Rio de Janeiro: IMPA, 2012. - video online
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.
Matematica.