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Matthew Kennedy awarded NSERC Discovery Accelerator Supplement

Wednesday, October 10, 2018

Associate Professor Matthew Kennedy received a $120,000 Discovery Accelerator Supplement from the Natural Sciences and Engineering Research Council (NSERC) for his work within the field of operator algebras.

Operator algebras have applications in physics, where they play a prominent role in quantum information theory, and to other areas of mathematics like group theory and the theory of dynamical systems. It was John von Neumann’s work on the mathematical foundations of quantum physics that first convinced mathematicians to view various structures arising in the theory of operator algebras as noncommutative counterparts of classical objects. It’s this philosophy that underlies Kennedy’s work.

“This supplement will allow me to develop collaborations by hosting experts in group theory and dynamics from around the world,” stated Kennedy. “I am grateful to NSERC for this additional funding.”

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.

“On behalf of the Department of Pure Mathematics, I would like to congratulate Matt,” said department chair David McKinnon. “His work is extremely exciting, and has attracted the interest of top researchers around the globe and across mathematics.”