Motives and dg-categories

In this lecture, I will explain how to construct a "motive" out of certain linear categories.
This will be applied to some standard derived categories of algebro-geometric origin
such as derived categories of schemes, categories of matrix factorizations, categories
of representations etc.
The case of matrix factorizations will be analysed more specifically in a second part
of the talk, for which our motivic construction provides new results relating matrix
factorization and vanishing cycles (including the positive and mixed characteristic settings).
(This is a joint work with A. Blanc, M. Robal and G. Vezzosi.)