Related papers: Quantum Sheaf Cohomology, a pr\'ecis

It is a sequel to (Wu in arXiv:2003.05187). In that paper, we introduce a notion called modified ideal sheaf in order to make an asymptotic estimate for the order of the cohomology group. Here we continue to a general discussion about this…

We give a natural filtration F on quantum cohomology QH(G/B) of G/B, which respects the quantum product structure. Its associated graded algebra is isomorphic to the tensor product of QH(G/P) and a corresponding graded algebra of QH(P/B)…

We introduce an equivariant version of contextuality with respect to a symmetry group, which comes with natural applications to quantum theory. In the equivariant setting, we construct cohomology classes that can detect contextuality. This…

We prove some extension theorems for analytic objects, in particular sections of a coherent sheaf, defined in semi q-coronae of a complex space. Semi q-coronae are domains whose boundary is the union of a Levi flat part, a q-pseudoconvex…

We prove that the quantum cohomology ring of any minuscule or cominuscule homogeneous space, once localized at the quantum parameter, has a non trivial involution mapping Schubert classes to multiples of Schubert classes. This can be stated…

We start by presenting a brief summary of fractional quantum mechanics, as means to convey a motivation towards fractional quantum cosmology. Subsequently, such application is made concrete with the assistance of a case study. Specifically,…

We describe a cohomological framework for measurement based quantum computation, in which symmetry plays a central role. Therein, the essential information about the computational output is contained in topological invariants, namely…

Two-dimensional (2,2) supersymmetric nonlinear sigma models can be described in (2,2), (2,1) or (1,1) superspaces. Each description emphasizes different aspects of generalized K\"ahler geometry. We investigate the reduction from (2,2) to…

We show that every sheaf on the site of smooth manifolds with values in a stable (infinity,1)-category (like spectra or chain complexes) gives rise to a differential cohomology diagram and a homotopy formula, which are common features of…

We show for any oriented surface, possibly with a boundary, how to generalize Kramers-Wannier duality to the world of quantum groups. The generalization is motivated by quantization of Poisson-Lie T-duality from the string theory.…

We sketch a proof of a conjecture of [FFKM] that relates the geometric Eisenstein series sheaf with semi-infinite cohomology of the small quantum group with coefficients in the tilting module for the big quantum group.

A K-theoretic counterpart of quantum cohomology theory is discussed.

In a previous preprint (quant-ph/0012122) we introduced a ``contextual objectivity" formulation of quantum mechanics (QM). A central feature of this approach is to define the quantum state in physical rather than in mathematical terms, in…

The operation of tensor product of Cohomological Field Theories (or algebras over genus zero moduli operad) introduced in an earlier paper by the authors is described in full detail, and the proof of a theorem on additive relations between…

Let X be a smooth projective curve over a perfect field k of positive characteristic. This work investigates the relationship between stratified cohomology and group cohomology of the stratified fundamental group of X.

We construct dual descriptions of (0,2) gauged linear sigma models. In some cases, the dual is a (0,2) Landau-Ginzburg theory, while in other cases, it is a non-linear sigma model. The duality map defines an analogue of mirror symmetry for…

We give another proof of the generic semisimplicity of the big quantum cohomology of the symplectic isotropic Grassmannians IG(2,2n).

We review the status of (scalar) quantum field theory on curved spacetimes using a novel formulation in terms of non linear functionals over the smooth configuration fields. In particular, this entails also a new foundation of locally…

We introduce the quantum isomeric supercategory and the quantum affine isomeric supercategory. These diagrammatically defined supercategories, which can be viewed as isomeric analogues of the HOMFLYPT skein category and its affinization,…

The notion of sheaf quantization has many faces: an enhancement of the notion of constructible sheaves, the Betti counterpart of Fukaya--Floer theory, a topological realization of WKB-states in geometric quantization. The purpose of this…