Hodge theory of Log Singular Loci

• Applicant: Professor Dr. Helge Ruddat
• Subject Area: Mathematics
• Term: Funded in 2013
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 241231364

Mirror Symmetry is a deep relationship between different types of geometries: complex vs. symplectic geometry. It was discovered by physicists for Calabi-Yau geometries around 1990 and has since then led to very interesting mathematical results. Still many important questions remain open, e.g. a proof of the homological mirror symmetry conjecture and how mirror symmetry extends to more general geometries. Mile stones in the development of the subject relevant for this proposal have been most of all the work of Batyrev-Borisov, Strominger-Yau-Zaslow and Gross-Siebert. This project concerns a connection between these incorporating also very recent results on mirror symmetry for varieties of general type. In the Gross-Siebert approach, a mirror construction generalizing Batyrev-Borisov's, uses logarithmic geometry and toric degenerations. The singularities of the log structure had first been a road block in the development. Later however, it was shown that they constitute an important feature when a formal smoothing of a degenerate Calabi-Yau geometry was constructed. This project concerns an analysis of the Hodge theoretic aspects of this singular locus linking it with mirror symmetry for more general geometries.

• DFG Programme: Research Fellowships
• International Connection: Canada
• Host: Professor Dr. Ragnar-Olaf Buchweitz (†)