Related papers: Fourier-Mukai Transforms
We show that the Looijenga--Lunts--Verbitsky Lie algebra acting on the cohomology of a hyperk\"ahler variety is a derived invariant, and obtain from this a number of consequences for the action on cohomology of derived equivalences between…
A survey of some recent and important results which have to do with integrable equations and their relationship with the theory of surfaces is given. Some new results are also presented. The concept of the moving frame is examined, and it…
These notes briefly discuss Fourier transforms of finite measures and extensions of Fourier integrals to points in complex domains.
In this paper we present an approach to quadratic structures in derived algebraic geometry. We define derived n-shifted quadratic complexes, over derived affine stacks and over general derived stacks, and give several examples of those. We…
The paper contains a systematic theory of the one-dimensional Double Hecke algebra, including applications to the difference Fourier transform, Macdonald's polynomials, Gaussian sums at roots of unity, and Verlinde algebras. The main result…
Phylogenetic algebraic geometry is concerned with certain complex projective algebraic varieties derived from finite trees. Real positive points on these varieties represent probabilistic models of evolution. For small trees, we recover…
We develop a new framework of relative algebroids to address existence and classification problems of geometric structures subject to partial differential equations.
In this article, we introduce equivariant formal deformation theory of associative algebra morphisms. We introduce an equivariant deformation cohomology of associative algebra morphisms and using this we study the equivariant formal…
In this paper we study the representation dimension as well as the derived dimension of the path algebra of an artin algebra over a finite and acyclic quiver.
We obtain results related to boundedness of the growth of Fourier transform by the modulus of continuity on Damek-Ricci spaces. For noncompact riemannian symmetric spaces of rank one, analogues of all the results follow the same way.
We introduce an alternative formalization of curved spaces in which the concept of a pointwise affine space, as defined here, replaces that of a manifold. New or modified definitions of familiar notions from differential geometry such as…
The development of algorithmic fractal dimensions in this century has had many fruitful interactions with geometric measure theory, especially fractal geometry in Euclidean spaces. We survey these developments, with emphasis on connections…
We define a Fourier-Mukai transform for a triple consisting of two holomorphic vector bundles over an elliptic curve and a homomorphism between them. We prove that in some cases the transform preserves the natural stability condition for a…
We show that a large class of finite dimensional pointed Hopf algebras is quasi-isomorphic to their associated graded version coming from the coradical filtration, i.e. they are 2-cocycle deformations of the latter. This supports a slightly…
This is the first paper in a series of eight where in the first three we develop a systematic approach to the geometric algebras of multivectors and extensors, followed by five papers where those algebraic concepts are used in a novel…
We consider some integral-geometric quantities that have recently arisen in harmonic analysis and elsewhere, derive some sharp geometric inequalities relating them, and place them in a wider context.
A mixture of an historical article, and of a survey of recent developments, containing also a couple of new results.
In this survey, I suggest to approach the problem of functorial properties of quantum cohomology by drawing lessons from several versions of Mirror duality involving deformation spaces.
We review the basic ideas lying at the foundation of the recently developed theory of twisted symmetries of differential equations, and some of its developments.
In this paper, we will obtain new algebraic transformations of the $_2F_1$-hypergeometric functions. The main novelty in our approach is the interpretation of identities among $_2F_1$-hypergeometric functions as identities among automorphic…