相关论文: Goursat's (n+1)-Webs
In the first part, we give a self contained introduction to the theory of cyclic systems in n-dimensional space which can be considered as immersions into certain Grassmannians. We show how the (metric) geometries on spaces of constant…
We bound the second Chern class of the tangent sheaf of a codimension-one foliation. Equivalently, we bound the degree of the pure codimension-two part of the singular scheme. In particular, for a degree-$d$ foliation on the projective…
We provide a simple derivation of particle-vortex duality in d=2+1 dimensions. Our starting point is a relativistic form of flux attachment, designed to transmute the statistics of particles. From this seed, we derive a web of new…
We propose a class of intrinsic Gaussian processes (in-GPs) for interpolation, regression and classification on manifolds with a primary focus on complex constrained domains or irregular shaped spaces arising as subsets or submanifolds of…
We consider the Goursat problem in the plane for partial differential operators whose principal part is the $p$th power of the standard Laplace operator. The data is posed on a union of $2p$ distinct lines through the origin. We show that…
We give a careful general relativistic and (1+3)-covariant analysis of cosmological peculiar velocities induced by matter density perturbations in the presence of a cosmological constant. In our quasi-Newtonian approach, constraint…
We introduce the pro-tensor network, a categorification of the tensor network, as a fully rigorous yet graphically transparent framework for studying the collection of many many-body theories, which we dub many-many-body theory. We provide…
We first review the Coset Space Dimensional Reduction (CSDR) programme and present the best model constructed so far based on the $\mathcal{N} = 1$, $10$-dimensional $E_8$ gauge theory reduced over the nearly-K\"ahler manifold…
We study the quantum mechanics of a system of topologically interacting particles in 2+1 dimensions, which is described by coupling the particles to a Chern-Simons gauge field of an inhomogeneous group. Analysis of the phase space shows…
We first briefly review the Coset Space Dimensional Reduction (CSDR) programme and present the results of the best model so far, based on the $\mathcal{N} = 1$, $d = 10$, $E_8$ gauge theory reduced over the nearly-K\"ahler manifold…
There are only some exceptional CR dimensions and codimensions such that the geometries enjoy a discrete classification of the pointwise types of the homogeneous models. The cases of CR dimensions $n$ and codimensions $n^2$ are among the…
A new type of topological matter interactions involving second-rank antisymmetric tensor matter fields with an underlying $N_T \geq 1$ topological supersymmetry are proposed. The construction of the 4-dimensional, $N_T = 1$ Donaldson-Witten…
We show that known de Sitter solutions in extended gauged supergravity theories are interrelated via a web of supersymmetry-breaking truncations. In particular, all N=8 models reduce to a subset of the N=4 possibilities. Furthermore, a…
This paper considers gauge-invariant and covariant gravitational perturbations on arbitrary vacuum locally rotationally symmetric (LRS) class II space-times. Ultimately, we derive four decoupled equations governing four specific…
We discuss invertible and non-invertible topological condensation defects arising from gauging a discrete higher-form symmetry on a higher codimensional manifold in spacetime, which we define as higher gauging. A $q$-form symmetry is called…
For any d-web by curves in an ambiant n-dimensional manifold, we define a tautological connection on some associated bundle, whose curvature vanishes iff the web has a maximal (n-1)-rank. As an application we recover, with the help of a…
Our aim is to develop a general approach for the dynamics of material bodies of dimension d represented by a mater manifold of dimension (d + 1) embedded into the space-time. It can be declined for d = 0 (pointwise object), d = 1 (arch if…
Inverse energy cascade regime of two dimensional turbulence is investigated by means of high resolution numerical simulations. Numerical computations of conditional averages of transverse pressure gradient increments are found to be…
Define the complete n-complex on N vertices to be the n-skeleton of an (N-1)-simplex. We show that embeddings of sufficiently large complete n-complexes in R^{2n+1} necessarily exhibit complicated linking behaviour, thereby extending known…
We state and prove a topological recursion relation that expresses any genus-g Gromov-Witten invariant of a projective manifold with at least a (3g-1)-st power of a cotangent line class in terms of invariants with fewer cotangent line…