Roberto Hernandez Palomares
University of Waterloo
Title
Classical to Quantum through Operator Algebras
Abstract
Operator algebras were originally developed to capture the behavior of noncommuting variables that model observable quantities in quantum mechanics. Over the past century, this framework has helped reshape our understanding of fundamental ideas such as symmetry, locality, and information. In turn, many familiar mathematical structures such as groups, graphs, and spaces have found new quantum versions inspired by these developments. In this talk, I will give an overview of some of these quantum mathematical objects, highlighting their connections, applications, and my contributions to the field. I will also illustrate how tools from operator algebras and tensor categories provide a common language for studying both classical and quantum phenomena.
The talk is intended for a broad mathematical audience.