
Toric varieties form a class of possibly singular algebraic varieties that most geometers are familiar with. Intersection spaces are assigned to certain singular spaces to restore Poincaré duality and provide a generalized cohomology theory on singular spaces.
In this talk, I will explain the two concepts and show why it is good to examine intersection spaces of toric varieties and motivate the combination of the two concepts both from a theoretical (Poincaré duality) and an application (mirror symmetry) point of view.