相关论文: The quantum cohomology of homogeneous varieties

We reproduce the quantum cohomology of toric varieties (and of some hypersurfaces in projective spaces) as the cohomology of certain vertex algebras with differential. The deformation technique allows us to compute the cohomology of the…

We discuss a general quantum theoretical example of quantum cohomology and show that various mathematical aspects of quantum cohomology have quantum mechanical and also observable significance.

We compute the quantum cohomology relative to a Lagrangian submanifold in some complete intersections. For quadric hypersurfaces, we also give a full computation of the genus zero open Gromov-Witten invariants.

We study the quantum cohomology of (co)minuscule homogeneous varieties under a unified perspective. We show that three points Gromov-Witten invariants can always be interpreted as classical intersection numbers on auxiliary varieties. Our…

We describe recent work on positive descriptions of the structure constants of the cohomology of homogeneous spaces such as the Grassmannian, by degenerations and related methods. We give various extensions of these rules, some new and…

We construct an associative ring which is a deformation of the quantum cohomology ring of the projective plane. Just as the quantum cohomology encodes the incidence characteristic numbers of rational plane curves, the contact cohomology…

Lecture notes. Introduction to the cohomology of algebras, Lie algebras, Lie bialgebras and quantum groups. Contains a new derivation of the classification of classical r-matrices in terms of deformation cohomology, and a calculation of the…

We define a new cohomology for associative algebras which we compute for algebras with units.

The quantum cohomology algebra of a projective manifold X is the cohomology H(X,Q) endowed with a different algebra structure, which takes into account the geometry of rational curves in X. We show that this algebra takes a remarkably…

We describe a method for counting maps of curves of given genus (and variable moduli) to $\Bbb P^2$, essentially by splitting the $\Bbb P^2$ in two; then specialising to the case of genus 0 we show that the method of quantum cohomology may…

We describe recent progress on QH(G/P) with special emphasis of our own work.

Differential calculi are obtained for quantum homogeneous spaces by extending Woronowicz' approach to the present context. Representation theoretical properties of the differential calculi are investigated. Connections on quantum…

We introduce an equivariant version of Hochschild cohomology as the deformation cohomology to study equivariant deformations of associative algebras equipped with finite group actions.

Using the Kontsevich's moduli space of stable maps, we define the equivariant quantum cohomology for generalized flag varieties and make a rigorous computation of quantum cohomology of flag varieties.

We examine a few problems of enumerative geometry and present their solutions in the framework of deformed (quantum) cohomology rings.

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 general hyperplane sections of adjoint and coadjoint varieties. We show that these are the only sections of homogeneous varieties such that a maximal torus of the automorphism group of the ambient variety stabilizes…

Let X be a smooth projective variety. Using modified psi classes on the stack of genus zero stable maps to X, a new associative quantum product is constructed on the cohomology space of X. When X is a homogeneous variety, this structure…

We study finite dimensional representations of the quantum affine algebra, using geometry of quiver varieties introduced by the author. As an application, we obtain character formulas expressed in terms of intersection cohomologies of…

We implement in the formal language of homotopy type theory a new set of axioms called cohesion. Then we indicate how the resulting cohesive homotopy type theory naturally serves as a formal foundation for central concepts in quantum gauge…