Related papers: Modulation spaces with scaling symmetry
We consider some classical fibre bundles furnished with almost complex structures of twistor type, deduce their integrability in some cases and study \textit{self-holomorphic} sections of a \textit{symplectic} twistor space. With these we…
If we take a superintegrable Stackel system and make variables "faster" or "slower", that is equivalent to a trivial transformation of the Stackel matrix and potentials, then we obtain an infinite family of superintegrable systems with…
Derivatives and integration operators are well-studied examples of linear operators that commute with scaling up to a fixed multiplicative factor; i.e., they are scale-invariant. Fractional order derivatives (integration operators) also…
We present a construction of a family of non-periodic tilings using elementary tools such as modular arithmetic and vector geometry. These tilings exhibit a distinct type of structural regularity, which we term modulo-staggered rotational…
We construct monads for framed torsion-free sheaves on blow-ups of the complex projective plane at finitely many distinct points. Using these monads we prove that the moduli space of such sheaves is a smooth algebraic variety. Moreover we…
We study the wall-crossing for moduli spaces of coherent systems of dimension one and order one on a smooth projective variety over the complex numbers. We compute the topological Euler characteristic of the moduli spaces in the particular…
We introduce a notion of stability for sheaves with respect to several polarisations that generalises the usual notion of Gieseker-stability. We prove, under a boundedness assumption, which we show to hold on threefolds or for rank two…
Let $h_g^\infty$ be the space of harmonic functions in the unit ball that are bounded by some increasing radial function $g(r)$ with $\lim_{r\rightarrow 1} g(r)=+\infty$; these spaces are called growth spaces. We describe functions in…
We extend to a specific class of systems of nonlinear Schr\"odinger equations (NLS) the theory of asymptotic stability of ground states already proved for the scalar NLS. Here the key point is the choice of an adequate system of modulation…
Two quantum Hopf structures for the Schr\"odinger algebra as well as their corresponding differential-difference realizations are presented. For each case a (space or time) discretization of the Schr\"odinger equation is deduced and the…
Let $X$ be a smooth, irreducible, projective algebraic surface, and let $\alpha \in \mathbb{Q}[m]_{>0}$ be a polynomial. In this paper, we determine topological and geometric properties of the moduli space of $\alpha$-stable coherent…
It is shown that certain transformations on quiver-dimension vector pairs induce isomorphisms on the corresponding moduli spaces of quiver representations and map a stable dimension vector to a stable dimension vector. This result combined…
We construct the hyper-K\"ahler moduli space of framed monopoles over $\mathbb{R}^3$ for any connected, simply connected, compact, semisimple Lie group and arbitrary mass and charge, and hence symmetry breaking. In order to do so, we define…
We study the natural K\"ahler metrics on moduli spaces of stable oriented pairs in a very general framework, and we prove a universal formula expressing the K\"ahler class of such a moduli space in terms of characteristic classes of the…
We prove that bilinear fractional integral operators and similar multipliers are smoothing in the sense that they improve the regularity of functions. We also treat bilinear singular multiplier operators which preserve regularity and obtain…
We prove some semipositivity theorems for singular varieties coming from graded polarizable admissible variations of mixed Hodge structure. As an application, we obtain that the moduli functor of stable varieties is semipositive in the…
In the paper, it is given isomorphic classification of $F$-spaces of $log$-integrable measurable functions constructed using different measure spaces. At the same time, it is proved that such spaces are non-isometric.
Modular flow is a symmetry of the algebra of observables associated to spacetime regions. Being closely related to entanglement, it has played a key role in recent connections between information theory, QFT and gravity. However, little is…
In our recent papers, we studied semiclassical spectral problems for the Bochner-Schr\"odinger operator on a manifold of bounded geometry. We survey some results of these papers in the setting of the magnetic Schr\"odinger operator in the…
We construct moduli spaces of framed logarithmic connections and also moduli spaces of framed parabolic connections. It is shown that these moduli spaces possess a natural algebraic symplectic structure. We also give an upper bound of the…