|Date:||Fri, November 4, 2016|
|Place:||Lecture Hall, Research II|
Abstract: We will discuss combinatorial structure of spaces of complex polynomials. The latter are viewed as dynamical systems. A classical example is the Mandelbrot set which parameterizes complex quadratic polynomials with "interesting dynamics" up to affine conjugacy. A combinatorial model for the Mandelbrot set, which is also a conjectural topological model, is known. We address the issue of finding combinatorial models for spaces of higher degree polynomials. As in the quadratic case, it is useful first to model individual polynomials (combinatorial models for polynomials are provided by Thurston's laminations), and then use appropriate spaces of laminations to model the corresponding spaces of polynomials. This is a joint work with Alexander Blokh, Lex Oversteegen and Ross Ptacek.
The colloquium is preceded by tea from 13:45 in the Resnikoff Mathematics Common Room, Research I, 127.