PhD Thesis Defense

Adam Dor On, Department of Pure Mathematics, University of Waterloo

"Techniques in operator algebras: Classification, dilations and 
non-commutative boundaries"

In this talk we will see various techniques in operator algebras and operator systems. We begin with classification of non-self-adjoint and self-adjoint operator algebras constructed from certain Markov chains. We then transition to the study of non-commutative boundaries in the sense of Arveson, and use them to get interesting dilation results for families of operators associated to directed graphs. Finally, we discuss connections between operator systems, matrix convex sets and dilation theory, and use them to obtain scaled inclusion results for matrix convex sets.

MC 2009