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Extracting Gromov-Witten invariants of a conifold from semi-stable reduction and relative GW invariants of pairs
Chien-Hao Liu, Shing-Tung Yau
The study of open/closed string duality and large duality suggests a Gromov-Witten theory for conifolds that sits on the border of both a closed Gromov-Witten theory and an ope…
Geometric Aspects of the Moduli Space of Riemann Surfaces
Kefeng Liu, Xiaofeng Sun, Shin-Tung Yau
This is a survey of our recent results on the geometry of moduli spaces and Teichmuller spaces of Riemann surfaces appeared in math.DG/0403068 and math.DG/0409220. We introduce new…
The Existence of Supersymmetric String Theory with Torsion
Jun Li, Shing-Tung Yau
We derived an existence criterion to the Supersymmetric String Theory with Torsion proposed by Strominger and proved the existence of such theory for a class of Calabi-Yau threefol…
Canonical Metrics on the Moduli Space of Riemann Surfaces II
Kefeng Liu, Xiaofeng Sun, Shing-Tung Yau
In this paper we continue our study on the canonical metrics on the Teichmüller and the moduli space of Riemman surfaces. We first prove the equivalence of the Bergman metric and t…
A degeneration formula of Gromov-Witten invariants with respect to a curve class for degenerations from blow-ups
Chien-Hao Liu, Shing-Tung Yau
In two very detailed, technical, and fundamental works, Jun Li constructed a theory of Gromov-Witten invariants for a singular scheme of the gluing form that arises…
Topological String Partition Functions as Polynomials
Satoshi Yamaguchi, Shing-Tung Yau
We investigate the structure of the higher genus topological string amplitudes on the quintic hypersurface. It is shown that the partition functions of the higher genus than one ca…