Classifying finite and infinite C*-dynamics
Navn på bevillingshaver
James Gabe
Titel
Associate Professor
Institution
University of Southern Denmark
Beløb
DKK 7,000,000
År
2024
Bevillingstype
Semper Ardens: Accelerate
Hvad?
This project is in Pure Mathematics in an area of quantum theory known as Operator Algebras. The classification of C*-algebras (pronounced "C-star-algebras") is a major worldwide research initiative spanning over 30 years. This project focuses on classifying C*-dynamics, which encode how C*-algebras evolve in various situations, and will significantly deepen our understanding of these evolutions.
Hvorfor?
Classification is at the heart of many areas of science, such as the periodic table which classifies chemical elements. This project deals with classifying C*-dynamics, similar to writing up an infinitely large table describing these. Importantly, this allows us to refer to THE C*-dynamics with a given property, instead of always working with abstract C*-dynamics with such properties.
Hvordan?
My team will focus on classification in special cases, similar to building the periodic table one chemical element at a time. With an infinitely large table, this task would be never-ending. However, I will simultaneously develop more general classification theory, which essentially means discovering entire infinite rows in the table at the same time, and in combination we will gain deep insight.