Pure Maths Colloquium: Hyperbolicity of complex manifolds and Diophantine equations
10 October 2016 16:00 in CM221
Why do some equations have only finitely many integral solutions? For instance, Siegel showed that a polynomial equation in three variables with integral coefficients has only finitely many solutions if the associated complex space is hyperbolic. In this talk I will explain how Siegel's theorem fits in well with a conjecture of Serge Lang and Paul Vojta. The latter conjecture provides a framework which answers the above question by relating arithmetic properties of systems of polynomial equations to complex analysis.
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