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Infinite dimensional groups versus locally compact groups: some recent trends

4:00 pm Thursday, April 19th, 2012
Vladimir Pestov (University of Ottawa, Canada)

Typical "infinite-dimensional" groups include unitary groups of Hilbert spaces and of operator algebras, groups of homeomorphisms, groups of measure preserving transformations, etc. Does one expect their properties to be generalizations of those of locally compact groups, or, on the contrary, to go in the opposite direction? The answer is, neither. We will survey some recent general trends in the theory of "infinite-dimensional" groups, in order to show that in many aspects, their properties go in an "orthogonal" direction to the classical theory of locally compact groups.

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