Descent and equivalences in non-commutative geometry

Abstract: I will describe descent formalism in categorical non-commutative geometry which is geared towards constructions of Fourier–Mukai functors. The formalism allows one to carry out descent constructions in general algebraic and analytic frameworks without resorting to generators. I will discuss various applications, such as the connection to the classical Zariski and flat descents, constructions of Fukaya categories, and homological mirror symmetry. This is a joint work with Katzarkov and Kontsevich.