| Details: |
Dynamics of complex polynomials, and the associated connectedness loci have been an exciting area of research in the last few decades. The Mandelbrot set, which is the connectedness locus of quadratic polynomials, is the simplest object (though an extremely complicated set to study) in this category. It is well-known that the Mandelbrot set is universal; in particular, it contains infinitely many homeomorphic copies of itself.
The connectedness loci of higher degree polynomials turn out to be much more unwieldy, and several happy features of the Mandelbrot set fail to hold in the higher degree setting. We will focus on a specific example to illustrate some of the topological differences between the Mandelbrot set and its higher degree cousins. Time permitting, we will outline conformal obstructions to universality for higher degree connectedness loci. |