摘要: A hyperkahler manifold is a hinger dimensional analogue of K3 surfaces. Such manifolds have many interesting geometric properties and are among one type of the building blocks of manifolds with trivial first Chern classes together with torus and Calabi—Yau manifolds.

In the first talk, I will discuss the positivity of coefficients of the Riemann--Roch polynomial and also positivity of Todd classes. Such positivity results follows from a Lefschetz-type decomposition of the root of Todd genus via the Rozansky—Witten theory.

In the second talk, I will briefly introduce the Rozansky—Witten theory for hyperkahler manifolds.