arXiv:1210.5249 Noncommutative calculus and operads fra arXiv Front: math.KT av Boris Tsygan This is a survey of current and recent works on deformation quantization and index theorems.
arXiv:1206.1435 Three lectures on Algebraic Microlocal Analysis from arXiv Front: math.AG by Pierre Schapira These three lectures present some fundamental and classical aspects of microlocal analysis. Starting with the Sato’s microlocalization functor and the microsupport of sheaves, we then construct a microlocal analogue of the Hochschild homology for sheaves and apply it to recover index theorems for D-modules and elliptic pairs. In the third lecture, we construct the ind-sheaves of temperate and Whitney holomorphic functions and give some applications to the study of irregular holonomic D-modules.
nLab page on Index theorems