Self-Similarity and Branching in Group Theory

The Banff International Research Station will host top researchers in its workshop on "Self-Similarity and Branching in Group Theory" next week, October 12 - October 17, 2008. The importance of self-similarity and branching phenomena in group theory has recently come to the forefront. Self-similar groups are the algebraic counterparts to fractals. Fractals quite often arise as Julia sets of certain rational functions, say polynomials. For instance, the Basilica of Saint Mark fractal is the Julia set of the polynomial $z^2+1$. The famous Sierpinski gasket is also the Julia set of a rational function. To each such rational function, there is associated a self-similar group, which encodes algebraically the Julia set and the dynamics of the rational function on the Julia set. The study of self-similar groups has led to new insights and a better understanding of fractals and their related dynamics. A longstanding-problem concerning the rabbit fractal and the airplane fractal was solved via the method of self-similar groups. Self-similar groups also have interactions with Computer Science, since much of their structure can be encoded by finite state machines. These machines can be used in turn to produce the fractals.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the US National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnologí­a (CONACYT).

BIRS Scientific Director, Nassif Ghoussoub
E-mail: birs-director[@]birs.ca
http://www.birs.ca/~nassif