Grant: Discovery Grants Program - Individual

My research program introduces a new mathematical structure, called Arveson system, and commences an exhaustive investigation of its properties in relation to the study of product systems and E0-semigroups. All these objects occur naturally in the theory of noncommutative dynamics, where they dictate the irreversible time-evolutions of quantum systems, and establish correlations between the anisotropy of physical time and the dynamical behavior of certain operator algebras.*An Arveson system is a collection of involutive algebras A(r,s), indexed over all time intervals (r,s) with 0(r,t) splits associatively into the tensor product of the algebras A(r,s) and A(s,t) in a certain way, for every 00-semigroups acting on any von Neumann algebra.*The results of my research program aim to bring a new approach and a solid contribution to the study of noncommutative dynamics, which will surely strengthen Canada's international reputation in this active area of research.