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Showing 1 to 12 of 12 for “"Quantum Cohomology"”.
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Equivariant quantum cohomology and the geometric Satake equivalence
… has discovered relations between the equivariant quantum cohomology of symplectic resolutions and Casimir-type connections (among many other objects). We provide a new example of this theory in the setting of the affine Grassmannian, a fundamental space in the geometric Langlands program. More …
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Equivariant Quantum Cohomology of the Odd Symplectic Grassmannian
… to prove a Chevalley formula in the equivariant quantum cohomology of IG, i.e. a formula to multiply a Schubert class by the Schubert divisor class. This generalizes a formula of Pech in the case k = 2, and it gives an algorithm to calculate any quantum multiplication in the equivariant quantum …
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Quantum cohomology of a Hilbert scheme of a Hirzebruch surface
… use of the associativity law satisfied by quantum product, calculate other Gromov-Witten invariants sufficient for us to determine the structure of quantum cohomology ring of the Hilbert scheme. The novel point of this work is that we manage to avoid families of invariant curves with the …
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The moment graph for Bott-Samelson varieties and applications to quantum cohomology
… to compute a presentation for the small quantum cohomology ring of a particular Bott-Samelson variety in Type A.
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On the Quantum Cohomology of Fano Toric Manifolds and the Intersection Cohomology of Singular Symplectic Quotients
The second result computes the intersection cohomology of the singular symplectic reduced spaces. Let M be a closed symplectic manifold with a Hamiltonian S1-action defined on it and mu is the moment map. If 0 is a singular value of mu, the reduced space mu-1(0)/S1 is, in general, no longer an …
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Chiral Rings of Two-dimensional Field Theories with (0,2) Supersymmetry
… theories. As a special case, we study the quantum sheaf cohomology of Grassmannians as a deformation of the usual quantum cohomology. The deformation corresponds to a (0,2) deformation of the nonabelian gauged linear sigma model whose geometric phase is associated with the Grassmannian. …
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Low Dimensional Supersymmetric Gauge Theories and Mathematical Applications
… GLSM to calculate the ordinary and equivariant quantum cohomology of the space, matching results in the math literature. Then we discuss 3d gauge theories with Chern-Simons terms. We propose a complementary method to derive the quantum K-theory relations of projective spaces and Grassmannians …
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The affine Yangian of gl₁, and the infinitesimal Cherednik algebras
… considered in the work of Maulik-Okounkov on the quantum cohomology theory, see [MO]. We present a purely algebraic realization of these algebras by generators and relations. We discuss some families of their representations. A similarity with the representation theory of the quantum toroidal …
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Applications of gauged linear sigma models
… the Coulomb ring relations (the analogue of quantum cohomology ring relations). We also studied pure gauge theories, and provided evidence (at the level of these topologicalfield-theory-type computations) that each pure gauge theory (with simply-connected gauge group) flows in the IR to a free …
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Gauged Linear Sigma Model and Mirror Symmetry
… more examples with new formulas that render the quantum sheaf cohomology relations and other properties manifest. We also include unpublished results for counting deformation parameters. The third chapter is about mirror symmetry. In the first part of the third chapter, we propose an extension of …
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Gromov-Witten theory in dimensions two and three
… Secondly, we compute the C-equivariant quantum cohomology ring of Y, the minimal resolution of the DuVal singularity C2 /G where G is a finite subgroup of SU(2). The quantum product is expressed in terms of an ADE root system canonically associated to G. We generalize the resulting …
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Derived categories of coherent sheaves on rational homogeneous manifolds
… sequence in $D^b(Coh\, Y)$ if and only if the quantum cohomology of $Y$ is generically semisimple (the complete form of the conjecture also makes a prediction about the Gram matrix of such a collection). A proof of this conjecture would also support M. Kontsevich's homological mirror …