Multidimensional symbolic dynamics and C*-algebras
Navn på bevillingshaver
Kevin Aguyar Brix
Titel
Postdoctoral Fellow
Institution
University of Glasgow
Beløb
DKK 1,397,000
År
2023
Bevillingstype
Reintegration Fellowships
Hvad?
Dynamical systems is a mathematical theory of how a system evolves over time. Many important examples (such as the Ising model from statistical mechanics) are modelled in two or more dimensions, so it is important to develop appropriate tools that work in more than one dimension. This project uses the quantum mathematics of operator algebras (and C*-algebras) to do this.
Hvorfor?
Multidimensional dynamical systems have a very complex behaviour which makes even fundamental questions formally undecidable. It is therefore very difficult to make general descriptions of their behaviour. This project aims to introduce a new set of tools which aims to provide new insight into such dynamical systems.
Hvordan?
The novelty of this project comes from the use of operator algebras (the mathematics von Neumann introduced to formalise quantum mechanics a century ago) to solve problems in dynamical systems. The guiding philosophy is to replace dynamical information with static and noncommutative operators on Hilbert space.