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\textsc{Number Theory}
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\textsc{N16 Colloquium}
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\textit{Polynomial mappings}
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Mike Zieve\par
Institute for Advanced Study
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\textbf{Abstract:} I will present properties of polynomials mappings and generalizations.  I will first describe all polynomials f and g for wich there is a complex number c such that the orbits {c, f(c), F (f(c)), ...} and {c, g(c), g(g(c)),...} have infinite intersection.  I will also discuss a common generalization of this result and Mordell's conjecture (Faltings' theorem).  After this I will move to polynomial mappings over finite fields, with connections to curves having large automorphism groups and instances of a positive characteristic analogue of Riemann's existence theorem.\vspace{\fill}
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Tuesday, January 6, 2009, 4:00 pm\par
Mathematics and Science Center: W301
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\textsc{Mathematics and Computer Science}\par
\textsc{Emory University}
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