Algebraic Dynamics Seminar: Complex billiards in the Fermat hyperbola


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April 4, 2024 4:00 pm - 6:00 pm
Science Center 232

Max Weinreich - Harvard

Last summer, in this seminar, I introduced a dynamical system called "complex billiards" that extends the classical real billiards map to the setting of curves over algebraically closed fields. The dynamical degree of complex billiards is an invariant that describes the "algebraic entropy", or chaos, of the system. In my previous talk, I proved an upper bound on this dynamical degree. In this talk, we derive lower bounds on the dynamical degree (a more challenging problem) through a careful study of one very special billiard table, the Fermat hyperbola. Independently of this result, we construct an algebraically stable model for complex billiards in the Fermat hyperbola using a little bit of complex dynamics. It is NOT necessary to have attended (or to remember) the previous talk, as I will begin again with all the key definitions.

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