160 citations · 218 across the 17 of their papers we have counts for
18 papers
Towards Categorical Kähler Geometry
Fabian Haiden, Ludmil Katzarkov, Maxim Kontsevich +1
We outline the contours of an emerging theory of Kähler metrics in derived noncommutative geometry. This is a refinement of the theory of Bridgeland stability conditions encoding u…
Gluing abelian categories and stability conditions
Charalampos Evangelatos, Fabian Haiden
We study the support property for stability conditions obtained by gluing along semiorthogonal decompositions. Our main tool is a new gluing construction for abelian categories alo…
A counterexample to the Jordan-Hölder property for polarizable semiorthogonal decompositions
Fabian Haiden, Dongjian Wu
We show that the Jordan-Hölder property fails for polarizable semiorthogonal decompositions -- those where every factor admits a Bridgeland stability condition. Counterexamples exi…
Counting in Calabi--Yau categories, with applications to Hall algebras and knot polynomials
Mikhail Gorsky, Fabian Haiden
We show that homotopy cardinality -- a priori ill-defined for many dg-categories, including all periodic ones -- has a reasonable definition for even-dimensional Calabi--Yau (evenC…
The stability manifold of
Fabian Haiden, Benjamin Sung
We determine a full component of the space of stability conditions on where is an elliptic curve without complex multiplication. The component has complex dimension…
Perverse schobers, stability conditions and quadratic differentials II: relative graded Brauer graph algebras
Merlin Christ, Fabian Haiden, Yu Qiu
We introduce a class of dg-algebras which generalize the classical Brauer graph algebras. They are constructed from mixed-angulations of surfaces and often admit a (relative) Calab…
Perverse schobers, stability conditions and quadratic differentials I
Merlin Christ, Fabian Haiden, Yu Qiu
We develop a unified approach for identifying spaces of stability conditions of triangulated categories arising from weighted marked surfaces with moduli spaces of quadratic differ…
Braid group actions on branched coverings and full exceptional sequences
Wen Chang, Fabian Haiden, Sibylle Schroll
We relate full exceptional sequences in Fukaya categories of surfaces or equivalently in derived categories of graded gentle algebras to branched coverings over the disk, building…
Spectral networks and stability conditions for Fukaya categories with coefficients
Fabian Haiden, Ludmil Katzarkov, Carlos Simpson
Given a holomorphic family of Bridgeland stability conditions over a surface, we define a notion of spectral network which is an object in a Fukaya category of the surface with coe…
3-d Calabi--Yau categories for Teichmüller theory
Fabian Haiden
For a 3-dimensional Calabi-Yau -category is constructed such that a component of the space of Bridgeland stability conditions, $\mathrm{Sta…
On pseudo-Anosov autoequivalences
Yu-Wei Fan, Simion Filip, Fabian Haiden +2
Motivated by results of Thurston, we prove that any autoequivalence of a triangulated category induces a filtration by triangulated subcategories, provided the existence of Bridgel…
Flags and tangles
Fabian Haiden
We show that two constructions yield equivalent braided monoidal categories. The first is topological, based on Legendrian tangles and skein relations, while the second is algebrai…
Legendrian skein algebras and Hall algebras
Fabian Haiden
We compare two associative algebras which encode the "quantum topology" of Legendrian curves in contact threefolds of product type . The first is the skein algebr…
An extension of the Siegel space of complex abelian varieties and conjectures on stability structures
Fabian Haiden
We study semi--algebraic domains associated with symplectic tori and conjecturally identified with spaces of stability conditions on the Fukaya categories of these tori. Our motiva…
Iterated logarithms and gradient flows
Fabian Haiden, Ludmil Katzarkov, Maxim Kontsevich +1
We consider applications of the theory of balanced weight filtrations and iterated logarithms, initiated in arXiv:1706.01073, to PDEs. The main result is a complete description of…
Semistability, modular lattices, and iterated logarithms
Fabian Haiden, Ludmil Katzarkov, Maxim Kontsevich +1
We provide a complete description of the asymptotics of the gradient flow on the space of metrics on any semistable quiver representation. This involves a recursive construction of…
Flat surfaces and stability structures
Fabian Haiden, Ludmil Katzarkov, Maxim Kontsevich
We identify spaces of half-translation surfaces, equivalently complex curves with quadratic differential, with spaces of stability structures on Fukaya-type categories of punctured…
Dynamical systems and categories
George Dimitrov, Fabian Haiden, Ludmil Katzarkov +1
We study questions motivated by results in the classical theory of dynamical systems in the context of triangulated and A-infinity categories. First, entropy is defined for exact e…