# Polynomial Rings and Topological Strings

Murad Alim (Harvard)

18.07.2013 at 16:15

I will discuss the construction of a differential polynomial ring from the special
geometry of the moduli space of Calabi-Yau threefolds. The higher genus
topological string amplitudes can be expressed in terms of the generators of
this ring giving them a global description in the moduli space. They can be
furthermore computed recursively up to boundary data from the BCOV
anomaly equations. Special choices of the generators coincide with quasi
modular forms for geometries with duality groups for which these are known.
They provide a generalization thereof in the other cases. The action of an
involution exchanging two distinguished expansion points of the quasi modular
forms is interpreted as a duality of the topological string amplitudes. This is
based on joint work with Emanuel Scheidegger, Shing-Tung Yau and Jie
Zhou.