2.4k citations · 7k across the 65 of their papers we have counts for
70 papers
A quantum connection approach to rationality
Luiz Carazolli, Leonardo F. Cavenaghi, Ludmil Katzarkov +2
We extract rank and regularized exponents from cyclic generic factors of the quantum connection and show that these data persist under the birational comparisons considered here. A…
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…
Moduli of atoms of complex projective varieties
Maxim Kontsevich, Szilard Szabo
The category of constituent pieces of Dubrovin connection of varieties is introduced and shown to be representable in affine space.
Non-commutative cluster Lagrangians
Alexander B. Goncharov, Maxim Kontsevich
The space Loc(m,S) of rank m flat bundles on a closed surface S is K_2-symplectic. A threefold M bounding S gives rise a K_2-Lagrangian in Loc(m,S) given by the flat bundles on S e…
Atoms meet symbols
Leonardo F. Cavenaghi, Ludmil Katzarkov, Maxim Kontsevich
This paper introduces a novel framework for constructing invariants in -equivariant birational geometry by unifying two recent approaches: the theory of atoms recently developed…
Birational Invariants from Hodge Structures and Quantum Multiplication
Ludmil Katzarkov, Maxim Kontsevich, Tony Pantev +1
We introduce new invariants of smooth complex projective varieties, called Hodge atoms. Their construction combines rational Gromov-Witten invariants with classical Hodge theory an…