The complex genera, symmetric functions and multiple zeta values

Abstract

We examine the coefficients in front of Chern numbers for complex genera, and pay special attention to the ${\text{Td}}^{\frac{1}{2}}$-genus, the Γ-genus as well as the Todd genus. Some related geometric applications to hyper-Kähler and Calabi-Yau manifolds are discussed. Along this line and building on the work of Doubilet in 1970s, various Hoffman-type formulas for multiple-(star) zeta values and transition matrices among canonical bases of the ring of symmetric functions can be uniformly treated in a more general framework.