DFF grant for Asger Dag Törnquist

The project title is “Hyperfinite Borel dynamics, distributed computing, and local growth constraints”. Asger describes the project as follows:

“Dynamical systems is a broad term for the many research areas in mathematics where models of systems that evolve and change (with time, say) are developed. Examples of dynamical systems can be found everywhere in our world: stock markets, climate and weather systems, ocean currents, glaciers, planetary systems, etc.

A computer network, such as the internet, where billions of computers are connected by data connections used to exchange information, is also a dynamical system. When computers in a network are programmed to work together to solve problems, we often call this “distributed computing”. This technology is used to create highly stable and fail-safe computer systems, and it is also the background for blockchain technologies.

In the last three years or so, researchers in descriptive set theory, which is my field, have discovered a close connection between Borel dynamical systems and distributed algorithms. We have discovered that they are essentially two (very) different languages for talking about the same phenomenon.

My project is about three important unsolved problems in Borel dynamics, with a special focus on so-called “hyperfinite” Borel dynamical systems. Using the correspondence between Borel dynamical systems and distributed computing, it has become possible to investigate how various growth constraints and resource allocation constraints influence Borel dynamical systems, and this is giving us new tools to attack a group of unsolved problems in the area. "

Asger Dag Törnquist's grant is for four years, and a PhD student will be assigned to the project.