This paper surveys the recent advances concerning the relations between triangulated (or
derived) categories and their dg enhancements. We explain when some interesting …

In this paper we discuss different properties of noncommutative schemes over a field. We
define a noncommutative scheme as a differential graded category of a special type. We …

Abstract We prove Homological Mirror Symmetry for a smooth d d-dimensional Calabi–Yau
hypersurface in projective space, for any d ≥ 3 d≥ 3 (for example, d= 3 d= 3 is the quintic …

Spherical DG-functors Page 1 DOI 10.4171/JEMS/724 J. Eur. Math. Soc. 19, 2577–2656 c
European Mathematical Society 2017 Rina Anno · Timothy Logvinenko Spherical DG-functors …

We show that the derived category of any singularity over a field of characteristic 0 can be
embedded fully and faithfully into a smooth triangulated category that has a semiorthogonal …

This paper is about the Fukaya category of a Fano hypersurface X⊂ CP n X⊂CP^n.
Because these symplectic manifolds are monotone, both the analysis and the algebra …

We study the space of stability conditions on the total space of the canonical bundle over the
projective plane. We explicitly describe a chamber of geometric stability conditions and …

We study a class of Legendrian surfaces in contact five-folds by encoding their wavefronts
via planar combinatorial structures. We refer to these surfaces as Legendrian weaves, and …

In this paper we prove the smoothness of the moduli space of Landau–Ginzburg models. We
formulate and prove a Bogomolov–Tian–Todorov theorem for the deformations of Landau …

Equivalence of the Derived Category of a Variety with a Singularity Category Page 1 M. Umut
Isik (2013) “Equivalence of Derived Category and Singularity Category,” International …