higher geometry / derived geometry
geometric little (∞,1)-toposes
geometric big (∞,1)-toposes
function algebras on ∞-stacks?
derived smooth geometry
A symplectic orbifold is an orbifold with symplectic structure, hence like a symplectic manifold but possibly with singularities modeled on fixed points of local actions of finite groups of symplectomorphisms.
Leonor Godinho, Blowing Up Symplectic Orbifolds, Annals of Global Analysis and Geometry 20, 117–162 (2001) (doi:10.1023/A:1011628628835)
Weimin Chen, Resolving symplectic orbifolds with applications to finite group actions, Journal of Gökova Geometry Topology 12 (2018), 1-39 (arXiv:1708.09428)
Juan Ángel Rojo Carulli, Orbifolds and geometric structures (2019) (eprints.ucm.es/56824/)
On orbifold cohomology of symplectic orbifolds:
Vasily Dolgushev, Pavel Etingof, Hochschild cohomology of quantized symplectic orbifolds and the Chen-Ruan cohomology, Int. Math. Res. Not. 2005, no. 27, 1657-1688 (arXiv:math/0410562)
Tara Holm, Tomoo Matsumura, Equivariant cohomology for Hamiltonian torus actions on symplectic orbifolds, Transformation Groups 17, 717–746 (2012) (arXiv:1008.3315, doi:10.1007/s00031-012-9192-7)
Cheol-Hyun Cho, Mainak Poddar, Holomorphic orbi-discs and Lagrangian Floer cohomology of symplectic toric orbifolds, J. Differential Geom. Volume 98, Number 1 (2014), 21-116 (euclid:jdg/1406137695)
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