C∗-algebras (pronounced "C-star") are an important area of research in functional analysis, a branch of mathematics.
My area of research is Operator Algebras, which is part of functional analysis. Functional analysis is the study of spaces of functions and other Banach spaces, and is related to differential equations, linear algebra, topology and abstract algebra. More precisely, I study groupoid C*-algebras and K-theory. Groupoids are similar to groups, except that they have many units, and one can not compose just any two elements. Additional structure is necessary, like a topology and a family of measures, in order to define a groupoid C*-algebra, which sometimes looks like a set of (infinite) matrices with complex entries. K-theory is a generalized cohomology theory, which is used in algebraic topology in order to distinguish surfaces and other topological spaces. The methods in my research are also inspired from dynamical systems, and the applications are in quantum statistical mechanics.
My field of research is a branch of Analysis called Operator Algebras. It is an intriguing mixture of Analysis and infinite-dimensional linear algebra. It is a relatively new field that has its origins in the mathematical formalism of quantum mechanics. I am particularly interested in operator algebras which arise from dynamical systems.