Uniform Bounds of Families of Twists

Start: 02/15/2017 - 4:15pm
End  : 02/15/2017 - 5:15pm


Bianca Thompson (HMC)

The study of discrete dynamical systems boomed in the age of computing. The Mandelbrot set, created by iterating 0 in the function z^2+c  and allowing c to vary, gives us a wealth of questions to explore. We can ask about the number of rational preperiodic points (points whose iterates end in a cycle) for z^2+c. Can this number be uniform as we allow c to vary? It turns out this is a hard question to answer. Instead we will explore places where this question can be answered; twists of rational functions. 
Shanahan B460, Harvey Mudd

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