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Research Program

  1. Number theory, especially elliptic curves. Arithmetic properties of elliptic curves over a number field or a function field, like the rank of the Mordell- Weil group, the conductor, associated Galois representations, as well as applications to Diophantine equations, coding theory and arithmetic algebraic geometry, are the objects of study.
  2. Ordinary differential equations. This concerns algebraic, analytic (e.g., mul- tisummability) and algorithmic aspects of linear differential and linear differ- ence equations; differential Galois theory and its applications, in particular to symbolic (algorithmic) solvability of equations; differential equations having the Painlevé property.
  3. Algebraic geometry related with curves, surfaces and threefolds: the maximal number of points on a curve of given genus over a given finite field; parametrizations of special rational surfaces, (history of) ruled surfaces, geometrical models, algebraic cycles.
  4. Drinfeld modules. This concerns a theory in positive characteristic which has similarities with the theory of elliptic curves and Abelian varieties.

Overview of scientific results

See the list of publications.