Complex Analysis, Dynamics and Geometry Seminar

The combinatorial structure of the Mandelbrot set has been studied by many people, notably in terms of minor laminations, by W.Thurston, the pinched disk model, by Douady and Hubbard, and orbit portraits, by Milnor. In this talk, we give an overview of the work of Schleicher, who used internal addresses to describe the combinatorial structure of the Mandelbrot set in an efficient way. We shall encounter the concept of kneading sequences of degree 2, and prove that they are equivalent to internal addresses. The latter part of the talk will be focussed on kneading sequences of general degree d, and discuss the problem of their admissibility, following the thesis of A.Kaffl. Speaker(s): Malavika Mukundan (U(M))