Colloquium Mathematics - Dr. E. Nijholt

Title: Exotic Forms of Symmetry in Network Dynamical Systems

Abstract:

Networks play a major role in science and engineering. Of particular importance is the time evolution of such systems - how does the structure of the network influence its behaviour? Even though dynamical systems theory (the study of time-dependent systems) is a well developed field of mathematics, network dynamical systems remain far less understood. The main reason for this is that a network structure is often ignored by most established tools from dynamical systems theory. Hence, there is a need for new techniques that are tailor-made to the network setting. I will present an exciting new way of viewing networks, based on a description in terms of "exotic forms of symmetry". It will turn out that a very important class of tools, the so-called reduction techniques, can now be adapted to network systems.