Concept
Cotangent bundle
Related publications (33)
Symplectic Dynamical Low Rank approximation of wave equations with random parameters
Fabio Nobile, Eleonora Musharbash
In this paper we propose a dynamical low-rank strategy for the approximation of second order wave equations with random parameters. The governing equation is rewritten in Hamiltonian form and the approximate solution is expanded over a set of dynamica ...
2017MATHICSE Technical Report : Symplectic dynamical low rank approximation of wave equations with random parameters
Fabio Nobile, Eleonora Musharbash, Eva Vidlicková
In this paper we propose a dynamical low-rank strategy for the approximation of second order wave equations with random parameters. The governing equation is rewritten in Hamiltonian form and the approximate solution is expanded over a set of 2S dynamical ...
MATHICSE2017Fréchet means in Wasserstein space
This work studies the problem of statistical inference for Fréchet means in the Wasserstein space of measures on Euclidean spaces, . This question arises naturally from the problem of separating amplitude and phase variation i ...
EPFL2017Dynamical Low Rank approximation of PDEs with random parameters
In this work, we focus on the Dynamical Low Rank (DLR) approximation of PDEs equations with random parameters. This can be interpreted as a reduced basis method, where the approximate solution is expanded in separable form over a set of few deterministic b ...
EPFL2017L-2-cohomology and complete Hamiltonian manifolds
A classical theorem of Frankel for compact Kahler manifolds states that a Kahler S-1-action is Hamiltonian if and only if it has fixed points. We prove a metatheorem which says that when the Hodge theory holds on non-compact manifolds, Frankel's theorem st ...
Elsevier2015Hilbert Schemes as Moduli of Higgs Bundles and Local Systems
We construct five families of 2D moduli spaces of parabolic Higgs bundles (respectively, local systems) by taking the equivariant Hilbert scheme of a certain finite group acting on the cotangent bundle of an elliptic curve (respectively, twisted cotangent ...
Oxford University Press2014The second order pullback equation
Bernard Dacorogna, Olivier Kneuss, Gyula Csató
Let f, g be two closed k-forms over R-n. The pullback equation studies the existence of a diffeomorphism phi : R-n -> R-n such that phi*(g) = f. We prove two types of results. The first one sharpens some of the existing regularity results. The second one d ...
Springer2014Extensions of Lie-Rinehart algebras and cotangent bundle reduction
Let Q denote a smooth manifold acted upon smoothly by a Lie group G. The G-action lifts to an action on the total space TQ of the cotangent bundle of Q and hence on the standard symplectic Poisson algebra of smooth functions on TQ. The Poisson algebra of ...
Oxford University Press2013Tangent space estimation for smooth embeddings of Riemannian manifolds
Pascal Frossard, Elif Vural, Hemant Tyagi
Numerous dimensionality reduction problems in data analysis involve the recovery of low-dimensional models or the learning of manifolds underlying sets of data. Many manifold learning methods require the estimation of the tangent space of the manifold at a ...
2013Equivariant K-theory of GKM bundles
Given a fiber bundle of GKM spaces, pi: M -> B, we analyze the structure of the equivariant K-ring of M as a module over the equivariant K-ring of B by translating the fiber bundle, pi, into a fiber bundle of GKM graphs and constructing, by combinatorial t ...
Springer Netherlands2013