An NWO TOP1-grant worth up to € 500,000 has been awarded to Han Peters and Guus Regts for their project ‘Methods from complex dynamics for locating zeros of graphs polynomials'. In the project, two PhD students will be involved.
The project combines elements from graph theory, complex analysis and dynamical systems, and is motivated by problems in complexity theory and statistical physics. The goal is to use and develop techniques in complex dynamical systems to solve open problems in graph theory regarding the location of zeros for graph polynomials. Examples of such graph polynomials include the partition function of the Potts model, the Ising model, the independence polynomial and the chromatic polynomial. Renormalization on recursively defined graphs induces iteration problems for rational maps in one or several complex variables. While the theory in one variable is quite well understood, in several variables many of the tools still remain to be developed.