On Calabi-Yau manifolds in the Hirzebruch problem for SU-bordism

Toric topology provides us with a new geometric approach to calculations with SU-bordism that allows to represent generators of the SU-bordism ring with 2 reversed and other important SU-bordism classes by quasitoric manifolds and Calabi–Yau hypersurfaces in toric Fano varieties. This approach will be discussed in my talk. The talk is based on the joint works with George Chernykh, Zhi Lu, and Taras Panov.