Mathematical Sciences: Index Theory and K-Theory of Group C*-Algebras

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Higson will continue his study of several problems related to Baum-Connes conjecture which asserts that for a locally compact group G, the K-theory of the reduced C*-algebra of G is equivariant to the K-theory of its universal proper G-space. This investigation will involve the use of an index theorem for proper actions, elliptic operators on buildings, and equivariant E-theory. This is part of the more general K-theory for operator algebras. The general area of mathematics of this project has its basis in the theory of algebras of Hilbert space operators. Operators can be thought of as finite or infinite matrices of complex numbers. Special types of operators are often put together in an algebra, naturally called an operator algebra. These seemingly abstract objects have a surprising variety of applications. For example, they play a key role in knot theory, which in turn is currently being used to study the structure of DNA. **//