Mathematical Sciences: Operator Algebras and Noncommutative Topology

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Professor Blackadar will continue his work on a wide range of problems concerning the structure of operator algebras and noncommutative algebraic topology. Specific topics to be studied are: (i) structure of inductive limits of homogeneous C*- algebras, (ii) nonstable K-theory and the fundamental comparability question, and (iii) existence and properties of cohomology theories on C*-algebras. The notion of a C* algebra is an abstraction of the idea of a family of linear transformations on a space. These transformations can also be thought of as having values in the states of the space, and the property of this family which is responsible for the symbol * is that the algebra is generated by transformations whose values in these states are real numbers. The fact that these objects appear naturally in many branches of mathematics and physics make them important to study.