35 citations · 72 across the 13 of their papers we have counts for
14 papers
An invitation to singular foliations
Camille Laurent-Gengoux, Ruben Louis, Leonid Ryvkin
These lecture notes attempt to invite the reader towards the theory of singular foliations, both smooth and holomorphic. In addition to a systematic review of the foundations, and…
Focusing on gap lengths in the noisy violinist chip-firing problem
Leonid Ryvkin
We encode the states in the noisy violinist chip-firing problem into a sequence of gap lengths, and use this gap-focused perspective to reprove certain statements about final state…
Reduction of -Algebras of Observables on Multisymplectic Manifolds
Casey Blacker, Antonio Michele Miti, Leonid Ryvkin
We develop a reduction scheme for the -algebra of observables on a premultisymplectic manifold in the presence of a compatible Lie algebra action $\mathfrak{g}\cu…
On Dirac structures admitting a variational approach
Oscar Cosserat, Camille Laurent-Gengoux, Alexei Kotov +2
We discuss the notion of basic cohomology for Dirac structures and, more generally, Lie algebroids. We then use this notion to characterize the obstruction to a variational formula…
The -algebra of a symplectic manifold
Bas Janssens, Leonid Ryvkin, Cornelia Vizman
We construct an -algebra on the truncated canonical homology complex of a symplectic manifold, which naturally projects to the universal central extension of the Lie alge…
The neighbourhood of a singular leaf
Camille Laurent-Gengoux, Leonid Ryvkin
An important result for regular foliations is their formal semi-local triviality near simply connected leaves. We extend this result to singular foliations for all 2-connected leav…
On the extension problem for weak moment maps
Leyli Mammadova, Leonid Ryvkin
We compare existence and equivariance phenomena for weak moment maps and homotopy moment maps in multisymplectic geometry.
The holonomy of a singular leaf
Camille Laurent-Gengoux, Leonid Ryvkin
We introduce the holonomy of a singular leaf of a singular foliation as a sequence of group morphisms from to the of the universal Lie -algebroid of…
Multisymplectic actions of compact Lie groups on spheres
Antonio Michele Miti, Leonid Ryvkin
We investigate the existence of homotopy comoment maps (comoments) for high-dimensional spheres seen as multisymplectic manifolds. Especially, we solve the existence problem for co…
An invitation to multisymplectic geometry
Leonid Ryvkin, Tilmann Wurzbacher
In this article we study multisymplectic geometry, i.e., the geometry of manifolds with a non-degenerate, closed differential form. First we describe the transition from Lagrangian…
Conserved quantities on multisymplectic manifolds
Leonid Ryvkin, Tilmann Wurzbacher, Marco Zambon
Given a vector field on a manifold M, we define a globally conserved quantity to be a differential form whose Lie derivative is exact. Integrals of conserved quantities over suitab…
Linear orbits of alternating forms on real vector spaces
Leonid Ryvkin
In this note we complete the calculation of the number of -orbits on , by treating the cases and not covered in the lite…
A multisymplectic manifold not covered by Darboux charts
Leonid Ryvkin
The Darboux theorem in symplectic geometry implies that any two points in a connected symplectic manifold have neighbourhoods symplectomorphic to each other. The impossibility of s…
Existence and unicity of co-moments in multisymplectic geometry
Leonid Ryvkin, Tilmann Wurzbacher
Given a multisymplectic manifold and a Lie algebra acting on it by infinitesimal symmetries, Fregier-Rogers-Zambon define a homotopy (co-)moment as an $L_{\infty…