The paper by Maxim Kontsevich and Yan Soibelman explores the concept of "generalized Donaldson-Thomas invariants" for non-commutative 3-dimensional Calabi-Yau varieties. The authors introduce the notion of stability conditions on these categories, which are encoded into a choice of polarization. They define motivic Donaldson-Thomas invariants, which take values in Grothendieck groups of algebraic varieties, and discuss their quasi-classical limit, leading to numerical DT-invariants. The paper also delves into the multiplicative wall-crossing formula, which describes how these invariants change when crossing certain "walls" in the space of stability conditions. This formula is expressed in terms of graded Lie algebras and is shown to be related to symplectic transformations on a double torus. The authors further explore the connection between these invariants and motivic functions, Milnor fibers, and orientation data. They conjecture that the numerical DT-invariants satisfy integrality properties and discuss the implications of these conjectures. The paper concludes with a detailed analysis of the case of 3-dimensional Calabi-Yau categories endowed with spherical collections, showing that cluster transformations naturally arise as birational symplectomorphisms of the double torus.The paper by Maxim Kontsevich and Yan Soibelman explores the concept of "generalized Donaldson-Thomas invariants" for non-commutative 3-dimensional Calabi-Yau varieties. The authors introduce the notion of stability conditions on these categories, which are encoded into a choice of polarization. They define motivic Donaldson-Thomas invariants, which take values in Grothendieck groups of algebraic varieties, and discuss their quasi-classical limit, leading to numerical DT-invariants. The paper also delves into the multiplicative wall-crossing formula, which describes how these invariants change when crossing certain "walls" in the space of stability conditions. This formula is expressed in terms of graded Lie algebras and is shown to be related to symplectic transformations on a double torus. The authors further explore the connection between these invariants and motivic functions, Milnor fibers, and orientation data. They conjecture that the numerical DT-invariants satisfy integrality properties and discuss the implications of these conjectures. The paper concludes with a detailed analysis of the case of 3-dimensional Calabi-Yau categories endowed with spherical collections, showing that cluster transformations naturally arise as birational symplectomorphisms of the double torus.