Stringy Euler numbers of toric Calabi-Yau hypersurfaces

The talk is devoted to stringy invariants of singular algebraic varieties and their applications in birational geometry and mirror symmetry. Projective Calabi-Yau models of non-degenerate affine hypersurfaces in algebraic torus provide simplest examples of explicit combinatorial formulas for stringy invariants. I explain some recent results and open questions motivated by different mirror symmetry constructions.