Seminar

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The global dynamics of a rational map f is controlled by the orbits of its critical points. We say that f is postcritically-finite if each of its critical points has finite orbit. In this case, we may encode the orbits of the critical points of f by a finite graph, called the ramification portrait of f. Such graphs have immediate restrictions that arise from considerations of local degrees and the Riemann-Hurwitz formula. We will discuss a recent paper by Floyd-Kim-Koch-Parry-Saenz which shows that in the polynomial setting these conditions are also sufficient for an abstract portrait to be realized as the ramification portrait of a postcritically-finite polynomial.