Related papers: Framed quiver moduli, cohomology, and quantum grou…
We develop a theory of $\phi$-coordinated (quasi) modules for a nonlocal vertex algebra and we establish a conceptual construction of nonlocal vertex algebras and their $\phi$-coordinated (quasi) modules, where $\phi$ is what we call an…
We prove that the moduli spaces of framed bundles over a smooth projective curve are rational. We compute the Brauer group of these moduli spaces to be zero under some assumption on the stability parameter.
When filtering a topological space by a single parameter, the theory of quiver representations provides a complete framework for decomposing the resulting persistence module to obtain its barcode. This is achieved by interpreting the…
The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…
Let V be the space of 2x2x2 complex hypermatrices, endowed with the natural group action of GL=GL(2,C)^3. The category of GL-equivariant coherent D-modules on V is equivalent to the category of representations of a quiver with relations. In…
We study the relationship between two stratifications on parameter spaces for coherent sheaves and for quiver representations: a stratification by Harder-Narasimhan types and a stratification arising from the geometric invariant theory…
We prove that in a stable range, the rational cohomology of the moduli space of curves with level structures is the same as that of the ordinary moduli space of curves.
We introduce the notion of being cohomologically complete for objects of the derived category of sheaves of $Z[\hbar]$-modules on a topological space. Then we consider a $Z[\hbar]$-algebra satisfying some suitable conditions and prove…
The role of quantum groups and braid groups in the description of Standard Model particles is discussed. Some recent results on the use of the quantum group $SU_q(3)$ as a flavour symmetry are reviewed and a connection between two…
Building on earlier work, we further develop a formalism based on the mathematical theory of frames that defines a set of possible phase-space or quasi-probability representations of finite-dimensional quantum systems. We prove that an…
The moduli spaces of stable quasimaps unify various moduli appearing in the study of Gromov-Witten Theory. This note is a survey article on the moduli of stable quasimaps, based on joint papers with Ciocan-Fontanine and Maulik as well as…
The topic of quantum reference frames (QRFs) has attracted a great deal of attention in the recent literature. Potentially, the correct description of such frames is important for both the technological applications of quantum mechanics and…
The aim of this article is to give a concise algebraic treatment of the modular symbols formalism, generalised from modular curves to Hecke triangle surfaces. A sketch is included of how the modular symbols formalism gives rise to the…
There exist many attempts to define a Wigner function for qudits, each of them coming with its advantages and limitations. The existing finite versions have simple definitions, but they are artificial in their construction and do not allow…
An equivariant stable birational invariant of an action of a finite group on a smooth projective variety is the first cohomology group of the Picard module. Bogomolov-Prokhorov and Shinder computed this for actions of cyclic groups on…
We define a cotriple (co)homology of crossed modules with coefficients in a $\pi_1$-module. We prove its general properties, including the connection with the existing cotriple theories on crossed modules. We establish the relationship with…
This paper defines coherent manifolds and discusses their properties and their application in quantum mechanics. Every coherent manifold with a large group of symmetries gives rise to a Hilbert space, the completed quantum space of $Z$,…
The tight frames can be regarded as a particular case of POVMs (positive operator-valued measures describing generalized measurements), namely the case when all the operators are rank-one. Each orthonormal basis is a tight frame, and every…
We introduce an infinite family of quiver representation-valued invariants of classical, virtual and surface-knots and links associated to a choice of finite biquandle, commutative unital ring, biquandle module and set of biquandle…
Symmetries of finite Heisenberg groups represent an important tool for the study of deeper structure of finite-dimensional quantum mechanics. This short contribution presents extension of previous investigations to composite quantum systems…