The aim of this proposal is to investigate asymptotic invariants of linear systems on projective varieties, and their applications to polyhedral combinatorics. Beside cohomological invariants of such systems, we also intend to study notions coming from higher-dimensional geometry, which describe singularities of closed subschemes. Our research methods will include asymptotic invariants of linear systems, techniques from toric geometry and vanishing theorems for divisors.
We plan to achieve our objectives via an intensive training and scientific cooperation with the Renyi Institute, which offers expertise in areas complementing mine. Parallel to the scientific mentoring process, a strong emphasis is put on furthering certain skills complementary to scientific research, such as research management and presentation skills. All along, a special care is taken for professional independence and leadership. Algebraic geometry is a modern are of mathematics on the leading edge of research. With its plentiful applications (among them Wiles' proof of the Fermat conjecture) and inter-disciplinary connections its further development can significantly increase the potential of European mathematics.
Once achieved, our goals can have a strong fertilizing effect in several prestigious areas of mathematics, thus contribute to the competitiveness of the European Research Area. By connecting a world-renowned centre of algebraic geometry outside Europe, the project will effectively transfer state-of-the-art knowledge between various centres of excellence, to the advantage of European researchers.
Call for proposal
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