We study questions motivated by results in the classical theory of dynamical systems in the
context of triangulated and A∞-categories. First, entropy is defined for exact endofunctors …

Supersymmetric D-branes supported on the complex two-dimensional base S of the local
Calabi–Yau threefold KS are described by semi-stable coherent sheaves on S. Under …

BPS states in type II string compactified on a Calabi-Yau threefold can typically be
decomposed as moduli-dependent bound states of absolutely stable constituents, with a …

In this paper we introduce new categorical notions and give many examples. In an earlier
paper we proved that the Bridgeland stability space on the derived category of …

The “moduli space” of stability conditions is currently an important ingredient in the
framework of Homological Mirror Symmetry (HMS). It was introduced by T. Bridgeland …

Let X be a toric Del-Pezzo surface and let C rit (W)⊂(ℂ*) n be the solution scheme of the
Landau-Ginzburg system of equations. Denote by X the polar variety of X. Our aim in this …

Let X be a toric Fano manifold and denote by C rit (f X)⊂(C∗) n the solution scheme of the
corresponding Landau–Ginzburg system of equations. For toric Del-Pezzo surfaces and …

Let X be a toric Fano manifold given by a reflexive polytope Δ and let C rit (f)⊂(C*) s be the
solution scheme of the Landau–Ginzburg system associated with a Laurent polynomial fu …

For a toric Fano manifold $ X $ denote by $ Crit (X)\subset (\mathbb {C}^{\ast})^ n $ the
solution scheme of the Landau-Ginzburg system of equations of $ X $. Examples of toric …

Let $ X=\mathbb {P}(\mathcal {O} _ {\mathbb {P}^ s}\oplus\bigoplus_ {i= 1}^ r\mathcal {O} _
{\mathbb {P}^ s}(a_i)) $ be a Fano projective bundle over $\mathbb {P}^ s $ and denote by …