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Functions determined by a few preimages
【2012.12.21 2:30pm,C610】

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 2012-12-21 

  Colloquia & Seminars 

  Speaker

  Prof.Micheal Zieve,University of Michigan

  Title

  Functions determined by a few preimages

  Time

  2012.12.21 2:30pm

  Venue

  C610

  Abstract

      A remarkable result of Nevanlinna's asserts that a meromorphic function on the complex plane is uniquely determined by its preimages at any five prescribed points. I will present related results in which one know the preimages of some finite sets, rather than the preimages of points. At the same time, I will determine all polynomials f(x) and g(x) with algebraic coefficients for which the equation f(x)=g(y) has infinitely many solutions in some number field. The proofs use various novel Galois-theoretic arguments, including new types of applications of the classification of finite simple groups.

  Affiliation

    

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