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Abstract: A C*-algebra is a norm-closed self-adjoint subalgebra of the bounded linear operators on Hilbert space. K-theory is, roughly speaking, the algebraic topology these algebras. In 1960 James Glimm proved that C*-algebras obtained as nested unions n x n matrices could be classified up to isomorphism by an invariant which was later recognised as K-theory. This was a bit surprising, as algebraic topology certainly does not classify CW-complexes up to homeomorphism! Glimm's result was later extended to locally finite-dimensional C*-algebras by George Elliott, and this marked the beginning of what is now known as the Elliott Program, an effort to classify separable amenable C*-algebras using K-theoretic invariants. In this talk I will give an introduction both to K-theory for operator algebras and to the results of Glimm and Elliott, followed by a history to date of Elliott's program and its connections to dynamics.
The talk will be accessible to senior undergraduates.
This talk will be accessible to undergraduates.
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