Derived categories of singular projective varieties and finite dimensional algebras

We will describe recent progress on describing derived categories of coherent sheaves for certain singular projective varieties in terms of derived categories of finite dimensional algebras, which are typically noncommutative.
This is based on ongoing joint works with Yujiro Kawamata & Nebojsa Pavic and with Carlo Klapproth, Nebojsa Pavic & Evgeny Shinder.