A local-global principle in the dynamics of quadratic polynomials

11/18/2014 - 12:15pm
11/18/2014 - 1:10pm
David Krumm (CMC)

A major open problem in the field of arithmetic dynamics is a uniform boundedness conjecture formulated by Morton and Silverman in 1994. Sadly, despite many efforts, not even the simplest case of this conjecture has been proved yet. By work of Poonen this basic case has been reduced to an extremely simple statement about the possible periods of a rational number under iteration of a quadratic polynomial. In this talk we will discuss a new approach to proving Poonen’s conjecture by showing that the theory of quadratic dynamical systems is a rare case in which global behavior can be determined by purely local considerations.

Mudd Science Library 126, Pomona College

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