数学所周五学术报告—From isolated hypersurface singularities to F-manifolds, Frobenius manifolds and an enrichment of harmonic bundles
主 题: 数学所周五学术报告—From isolated hypersurface singularities to F-manifolds, Frobenius manifolds and an enrichment of harmonic bundles
报告人: Professor Claus Hertling (University of Mannheim, Germany)
时 间: 2017-03-03 15:00-16:00
地 点: 理科1号楼1114
Abstract: Universal families of holomorphic functions with isolated singularities have been studied within singularity theory since the early 70ies. Later they became important in theoretical physics. Their moduli spaces carry a rich geometry. First, they are F-manifolds, i.e. there is a multiplication on the holomorphic tangent bundle with an integrability property. Second, these can be enriched by some choice to Frobenius manifolds. Those play a role in mirror symmetry. Third, above such a moduli space times C, there is a natural holomorphic vector bundle with an irregular meromorphic connection, a real structure and a pairing which is called a variation of TERP structures or of non-commutative Hodge structures. It is equivalent to an enrichment of a harmonic bundle. I have Torelli conjectures and results about this, since long time for the mu-constant stratum, more recently also at semisimple points.