Matthew Kennedy

There are two major components to Kennedy’s research. The first concerns the relationship between the properties of a group or dynamical system and the properties of the corresponding operator algebra. A major advance in 2014 by Kennedy, in joint work with Professors Emmanuel Breuillard, Mehrdad Kalantar and Narutaka Ozawa, answered several important questions about the structure of operator algebras corresponding to groups.

The second component of Kennedy’s research concerns the development of a theory of noncommutative convexity, to serve as a framework for the study of objects arising from noncommutative mathematics. First proposed by Professor William Arveson in 1969, the field remained dormant for nearly 45 years until recent breakthroughs. Arveson himself made a breakthrough in 2008 and in 2013 Kennedy in joint work with Professor Kenneth Davidson settled the principal open problem in the area. These ideas have already found applications in quantum information theory, group theory, and semidefinite optimization.