Oscillating integrals and a generalization

• Antragsteller: Professor Dr. Claus Hertling
• Fachliche Zuordnung: Mathematik
• Förderung: Förderung von 2005 bis 2014
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 16442363

Givental worked out cases of mirror symmetry, in which the quantum cohomology of Fano manifolds is on one side, and oscillating integrals of holomorphic tame functions on affine manifolds are on the other side. These oscillating integrals generalize the period integrals leading to variations of Hodge structures. In fact, by work of Sabbah, they give rise to mixed Hodge structures. The first goal of the project is to study arithmetic properties of these oscillating integrals and of Sabbah´s mixed Hodge structures. This will enrich Givental´s mirror symmetry by incorporating the real structures and the mixed Hodge structures which live on both sides. It will also complete a conjecture of Dubrovin on the quantum cohomology of Fano manifolds. The second goal is to develop the structure theory of a generalization of oscillating integrals. It consists in the direct images of elementary D-modules and provides a very natural geometric class of D-modules with irregular singularities.

• DFG-Verfahren: Sachbeihilfen