Matings of Polynomials

Monday, January 21, 2013 at 1:00pm to 1:45pm

Bronfman Science Center, 105 18 Hoxsey St, Williamstown, MA 01267, USA

Matings of PolynomialsSarah Koch, Harvard University
Mathematics and Statistics Department Colloquium

Abstract: Given two suitable complex polynomial maps, we can construct a new dynamical system by mating the polynomials; that is, by gluing together the Julia sets of the polynomials in a dynamically meaningful way. In this talk, we focus on quadratic polynomials --- we begin with a brief discussion of the parameter space for quadratic polynomials (where the Mandelbrot set lives), we then define the mating of two quadratic polynomials, and finally we explore examples where the mating does exist, and examples where it does not. The operation of mating two polynomials was introduced by Douady and Hubbard in 1983.

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Mathematics & Statistics

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