The objectives of the proposal are to increase the mobility of researchers in Europe and provide a training of high quality for the proposer. The scientific project deals with diophantine geometry and transcendental methods in number theory.
We will focus on the question of effectivity concerning Siegel's celebrated finiteness theorem on integral points on algebraic curves. The proposed method lies on the famous abc conjecture on diophantine analysis, the Belyi function and etales coverings. In relation with this topic we will study the links between the linear forms in (elliptic) logarithms and the abc conjecture.
The second part of the research project is about counting the algebraic points on which a transcendental function takes algebraic values, with a control on the height and the degree. We are interested in uniform upper bounds with respect to the bound of the height as well as in the higher dimensional analogue of the problem.
Call for proposal
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