It is a classical result that for any dg algebra A, the pair of its Hochschild (co)homologies $(HH^\bullet (A), HH_\bullet (A))$ carries rich algebraic structures resembling the usual Cartan calculus, often referred to as the Tamarkin--Tsygan calculus. DG manifolds provide a useful geometric framework for describing spaces with singularities. In this talk, I will discuss the Tamarkin--Tsygan calculus associated with the dg algebra of a dg manifold and present a Duflo--Kontsevich type theorem in this setting. As applications to several important examples, we recover the Duflo theorem on the center of the universal enveloping algebra of a Lie algebra and Kontsevich's theorem on the Hochschild cohomology of complex manifolds, placing them under
a unified framework. This is joint work with Hsuan-Yi Liao and Mathieu Sti\'enon.
大談話会