Operator Algebras and Functional Analysis
The field of Operator Algebras and Functional Analysis is a very broad field drawing together a group of people with somewhat diverse interests who all share one common focus: the application of analysis in describing, understanding, and effectively applying mathematical structures. The most fruitful subfields of this area with the richest structure and most challenging problems are those which draw together a variety of structures into one integrated whole.
Functional analysis and operator theory holds an important position in modern mathematics, and many subjects have their foundations built on it; to mention just a few: quantum mechanics, partial differential equations, and numerical analysis, which is essential in all engineering applications.