|Professor: Min Ru, Professor, Department of Mathematics, University of Houston, USA|
|Title: Results related to F.T.A. in number theory, complex analysis and geometry
|Abstract: The fundamental theorem of algebra (F.T.A.) states that for every complex polynomial P, the equation P(z)=0 always has d solutions on the complex plane, counting multiplicities, where d is the degree of P.
In this talk, I’ll discuss the results related to F.T.A. in number theory, complex analysis and geometry. In particular, I’ll describe the integer solutions of the Fermat’s equation (Faltings’ theorem), and related Diophantine equations (Diophantine approximation); the Little Picard theorem in complex analysis (viewed as a generalization of F.T. A.)
and overall so-called Nevanlinna theory; how the Nevanlinna theory is related to Diophantine approximation. Finally, I’ll discuss the study of Gauss map of minimal surfaces as part of application of the Nevanlinna theory.