A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The paper explores scaling symmetries in symplectic geometry and their applications to central configurations.
Study of Hamiltonian boundary value problems with symplectic symmetries.
We develop a new approach, based on quantization methods, to study higher symmetries of invariant differential operators. We focus here on conformally invariant powers of the Laplacian over a conformally flat manifold and recover results of Eastwood, Leistner, Gover and Šilhan. In particular, conformally equivariant qu…
Study on symmetries and equilibria in Poisson manifolds, with applications to rigid body dynamics.
This work takes place over a conformally flat spin manifold (M,g). We prove existence and uniqueness of the conformally equivariant quantization valued in spinor differential operators, and provide an explicit formula for it when restricted to first order operators. The Poisson algebra of symbols is realized as a space…
The geometry that is defined by the scalars in couplings of Einstein-Maxwell theories in N=2 supergravity in 4 dimensions is denoted as special Kaehler geometry. There are several equivalent definitions, the most elegant ones involve the symplectic duality group. The original construction used conformal symmetry, which…
Proves integrability of dispersionless Hirota type equations in 4D implies symplectic Monge-Ampere property.
Researchers find higher symmetries in symplectic Dirac operator.
The paper introduces polarizations in symplectic and orthogonal settings.
In this paper, we study the blow-up of a locally conformal symplectic manifold.We show that there exists a locally conformal symplectic structure on the blow-up of a locally conformal symplectic manifold along a compact induced symplectic submanifold.
The study explores conformal symplectic foliations on closed manifolds, proving their existence in dimensions 5 and above.
The study constructs optimal tori on Fano manifolds and confirms mirror symmetry.
In this paper we will present Lagrangian and Hamiltonian -symplectic formalisms, we will recall the notions of symmetry and conservation law and we will define the notion of pseudosymmetry as a natural extension of symmetry. Using symmetries and pseudosymmetries, without the help of a Noether type theorem, we will o…
Symplectic structures simplified for compact manifolds.
New formulae derived for conformal symmetry breaking operators.
We obtain structure results for locally conformally symplectic Lie algebras. We classify locally conformally symplectic structures on four-dimensional Lie algebras and construct locally conformally symplectic structures on compact quotients of all four-dimensional connected and simply connected solvable Lie groups.
Convexity theorem for Hamiltonian actions on conformal symplectic manifolds.
Explains conformal symmetry with examples in geometry and analysis.
We study first and second order conformal symmetries of the Yamabe Laplacian on a general pseudo-Riemannian manifold and of the Paneitz operator on Einstein spaces. We show that first order conformal symmetries of the Yamabe operator induce second order conformal symmetries. We show that on an Einstein space every conf…
Extends Gromov non-squeezing to locally conformally symplectic structures.
Reduces cotangent bundles using symplectic methods.
Reduces LCS manifolds with symplectic actions, preserving conformal structure.
Classifies symplectic phase space deformations preserving angular momentum symmetry.
We present some examples of locally conformal symplectic structures of the first kind on compact nilmanifolds which do not admit Vaisman metrics. One of these examples does not admit locally conformal Kähler metrics and all the structures come from left-invariant locally conformal symplectic structures on the correspon…
The paper explores symmetries and conserved charges on pre-symplectic manifolds.
A study on the relation between the smooth structure of a symplectic homotopy K3 surface and its symplectic symmetries is initiated. A measurement of exoticness of a symplectic homotopy K3 surface is introduced, and the influence of an effective action of a K3 group via symplectic symmetries is investigated. It is show…
Characterizes density-valued symplectic forms on multisymplectic manifolds.
Develops a correspondence between symplectic orbits and Grassmannians.
Study symplectic cohomology of certain singularities using homological mirror symmetry.
Symmetries of Einstein-Weyl manifolds can be extended from boundary surfaces.
Introduces locally conformally symplectic and Kähler geometry.
On locally conformally flat manifolds we describe a construction which maps generalised conformal Killing tensors to differential operators which may act on any conformally weighted tensor bundle; the operators in the range have the property that they are symmetries of any natural conformally invariant differential ope…
Solves symplectic and conformal symplectic group actions equivalence problem.
Researchers develop Orlov-Schulman symmetries for self-dual conformal structures.
Inspired by the results on symmetries of the symplectic Dirac operator, we realize symplectic spinor fields and the symplectic Dirac operator in the framework of (the double cover of) homogeneous projective structure in two real dimensions. The symmetry group of the homogeneous model of the double cover of projective g…
Two reduction schemes for symplectic manifolds are shown equivalent.
We obtain an example of a compact locally conformal symplectic nilmanifold which admits no locally conformal Kähler metrics. This gives a new positive answer to a question raised by L. Ornea and M. Verbitsky.
Abstract: Generalized reduction methods for symmetries in graded geometry.
Locally symplectic structure found on Kerr space-time.
In this article we study Ammann tilings from the perspective of symplectic geometry. Ammann tilings are nonperiodic tilings that are related to quasicrystals with icosahedral symmetry. We associate to each Ammann tiling two explicitly constructed highly singular symplectic spaces and we show that they are diffeomorphic…
We show that the first-order symmetry operators of twistor spinors can be constructed from conformal Killing-Yano forms in conformally-flat backgrounds. We express the conditions on conformal Killing-Yano forms to obtain mutually commuting symmetry operators of twistor spinors. Conformal superalgebras which consist of …
Paper proves h-principles for symplectic structures and foliations.
We show that a certain symmetry exists in the stable irreducible decomposition of the Lie algebra consisting of symplectic derivations of the free Lie algebra generated by the first homology group of compact oriented surfaces.
We obtain universal models for several types of locally conformal symplectic manifolds via pullback or reduction. The relation with recent embedding results for locally conformal Kähler manifolds is discussed.
Study projective and almost conformally symplectic structures on manifolds.
The paper discusses reducing Hamiltonian systems by scaling and standard symmetries, leading to Kirillov Hamiltonian systems.
Paper reduces nonholonomic systems with symmetries.
We exhibit two three-parameter families of locally conformal symplectic forms on the solvmanifold considered in [1], and show, using the Hodge-de Rham theory for the Lichnerowicz cohomology that that they are not exact, i.e. their Lichnerowicz classes are non-trivial (Theorem 1). This has several import…