11 citations · 34 across the 7 of their papers we have counts for
8 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…
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…
Generators in formal deformations of categories
Anthony Blanc, Ludmil Katzarkov, Pranav Pandit
In this paper we use the theory of formal moduli problems developed by Lurie in order to study the space of formal deformations of a -linear -category for a field . O…
Calabi-Yau Structures, Spherical Functors, and Shifted Symplectic Structures
Ludmil Katzarkov, Pranav Pandit, Theodore Spaide
A categorical formalism is introduced for studying various features of the symplectic geometry of Lefschetz fibrations and the algebraic geometry of Tyurin degenerations. This appr…
Reduction for pre-buildings
Ludmil Katzarkov, Pranav Pandit, Carlos Simpson
Given an spectral curve over a simply connected Riemann surface, we describe in detail the reduction steps necessary to construct the core of a pre-building with versal har…
Constructing Buildings and Harmonic Maps
Ludmil Katzarkov, Alexander Noll, Pranav Pandit +1
In a continuation of our previous work, we outline a theory which should lead to the construction of a universal pre-building and versal building with a -harmonic map from a Rie…
Harmonic Maps to Buildings and Singular Perturbation Theory
Ludmil Katzarkov, Alexander Noll, Pranav Pandit +1
The notion of a universal building associated with a point in the Hitchin base is introduced. This is a building equipped with a harmonic map from a Riemann surface that is initial…