Gromov-Witten invariants via localization techniques

Gromov-Witten invariants play a crucial role in symplectic- and enumerative Geometry as well as topological String Theory. Essentially, theseinvariants are a count of (pseudo)holomorphic curves of a given genus,going through n-marked points on a symplectic manifold. In the last fewdecades, this has been a huge research topic for both physicists as well asmathematicians, and breakthroughs in calculation techniques have beenmade using Mirror Symmetry. We investigate and explicitly calculateclosed genus zero Gromov-Witten invariants of toric Calabi-Yau threefolds, namely O(−3) → P2 and the resolved conifold. This will be doneby using localization techniques, mirror symmetry and the so called diskpartition function