15 citations · 52 across the 24 of their papers we have counts for
14 papers · 1 filter
The shifted symplectic geometry of derived higher groupoids
Miquel Cueca, Florian Dorsch, Reyer Sjamaar +1
The main goal of this work is to introduce derived Lie n-groupoids and their shifted symplectic structures. We further define shifted lagrangian structures and prove that their com…
Symplectic reduction and a Darboux-Moser-Weinstein theorem for Lie algebroids
Yi Lin, Yiannis Loizides, Reyer Sjamaar +1
We extend the Marsden-Weinstein reduction theorem and the Darboux-Moser-Weinstein theorem to symplectic Lie algebroids. We also obtain a coisotropic embedding theorem for symplecti…
Riemannian foliations and geometric quantization
Yi Lin, Yiannis Loizides, Reyer Sjamaar +1
We introduce geometric quantization for constant rank presymplectic structures with Riemannian null foliation and compact leaf closure space. We prove a quantization-commutes-with-…
Log symplectic manifolds and
Yi Lin, Yiannis Loizides, Reyer Sjamaar +1
We show, under an orientation hypothesis, that a log symplectic manifold with simple normal crossing singularities has a stable almost complex structure, and hence is Spin. In…
The convexity package for Hamiltonian actions on conformal symplectic manifolds
Youming Chen, Reyer Sjamaar, Xiangdong Yang
Consider a Hamiltonian action of a compact connected Lie group on a conformal symplectic manifold. We prove a convexity theorem for the moment map under the assumption that the act…
Stacky Hamiltonian actions and symplectic reduction
Benjamin Hoffman, Reyer Sjamaar, Chenchang Zhu
We introduce the notion of a Hamiltonian action of an étale Lie group stack on an étale symplectic stack and establish versions of the Kirwan convexity theorem, the Meyer-Marsden-W…
Convexity properties of presymplectic moment maps
Yi Lin, Reyer Sjamaar
The convexity and Morse-theoretic properties of moment maps in symplectic geometry typically fail for presymplectic manifolds. We find a condition on presymplectic moment maps that…
Convexity theorems for varieties invariant under a Borel subgroup
Victor Guillemin, Reyer Sjamaar
Atiyah proved that the moment map image of the closure of an orbit of a complex torus action is convex. Brion generalized this result to actions of a complex reductive group. We ex…
Group-valued Implosion and Parabolic Structures
Jacques Hurtubise, Lisa Jeffrey, Reyer Sjamaar
The purpose of this paper is twofold. First we extend the notion of symplectic implosion to the category of quasi-Hamiltonian -manifolds, where is a simply connected compact…
Equivariant symplectic Hodge theory and the -lemma
Yi Lin, Reyer Sjamaar
Consider a Hamiltonian action of a compact Lie group on a symplectic manifold which has the strong Lefschetz property. We establish an equivariant version of the Merkulov-Guillemin…
A de Rham theorem for symplectic quotients
Reyer Sjamaar
We introduce a de Rham model for stratified spaces arising from symplectic reduction. It turns out that the reduced symplectic form and its powers give rise to well-defined cohomol…
Symplectic implosion
Victor Guillemin, Lisa Jeffrey, Reyer Sjamaar
Let be a compact Lie group. We introduce the process of symplectic implosion, which associates to every Hamiltonian -manifold a stratified space called the imploded cross-se…
Moment maps and Riemannian symmetric pairs
Luis O'Shea, Reyer Sjamaar
The main result of this paper is a ``real form'' of Kirwan's convexity theorem, which in the abelian case was proved earlier by Duistermaat. We apply our result to flag varieties o…
Coadjoint orbits, moment polytopes, and the Hilbert-Mumford criterion
Arkady Berenstein, Reyer Sjamaar
Consider a compact Lie group and a closed subgroup. Generalizing a result of Klyachko, we give a necessary and sufficient criterion for a coadjoint orbit of the subgroup to be cont…