Suggestion for Bachelor

The field of the proposed project is opinion dynamics which involves the mathematical modeling of how groups of agents (people) influence one anothers’ opinions. This is very much a cross-disciplinary field, involving work by physicists, computer scientists, robotics engineers and, of course, social scientists. Mathematically, it is still very young, with a shortage of rigorous theorems even at a very basic level. However, interest from mathematicians is slowly growing, and there are several people at this department working on various aspects of the field. More precisely, the proposed project is concerned with studying a class of models introduced by Rainer Hegselmann and Ulrich Krause 12-15 years ago. In its most well-known form, the Hegselmann-Krause model [1] posits that there are a finite number of agents, indexed by the integers 1, 2, . . . , n. Time is measured discretely, and the opinion of agent i at time t is represented by a real number xt(i). At each time step, all agents simoultaneously update their opinions according to the formula