152 citations · 245 across the 8 of their papers we have counts for
12 papers
Connectedness in weighted consensus division of graphical cakes between two agents
Josef Hanke, Ana Rita Pires
Austin's moving knife procedure was originally introduced to find a consensus division of an interval/circular cake between two agents, each of whom believes that they receive exac…
A classification of infinite staircases for Hirzebruch surfaces
Nicki Magill, Ana Rita Pires, Morgan Weiler
The ellipsoid embedding function of a symplectic manifold gives the smallest amount by which the symplectic form must be scaled in order for a standard ellipsoid of the given eccen…
Infinite staircases for Hirzebruch surfaces
Maria Bertozzi, Tara S. Holm, Emily Maw +4
We consider the embedding capacity functions for symplectic embeddings of ellipsoids of eccentricity into the family of nontrivial rational Hirzebruch surfaces $H_…
On infinite staircases in toric symplectic four-manifolds
Dan Cristofaro-Gardiner, Tara S. Holm, Alessia Mandini +1
An influential result of McDuff and Schlenk asserts that the function that encodes when a four-dimensional symplectic ellipsoid can be embedded into a four-dimensional ball has a r…
Convexity for Hamiltonian torus actions on -symplectic manifolds
Victor Guillemin, Eva Miranda, Ana Rita Pires +1
In [GMPS] we proved that the moment map image of a -symplectic toric manifold is a convex -polytope. In this paper we obtain convexity results for the more general case of no…
The fundamental group and Betti numbers of toric origami manifolds
Tara S. Holm, Ana Rita Pires
Toric origami manifolds are characterized by origami templates, which are combinatorial models built by gluing polytopes together along facets. In this paper, we examine the topolo…
Toric actions on b-symplectic manifolds
Victor Guillemin, Eva Miranda, Ana Rita Pires +1
We study Hamiltonian actions on -symplectic manifolds with a focus on the effective case of half the dimension of the manifold. In particular, we prove a Delzant-type theorem th…
The topology of toric origami manifolds
Tara Holm, Ana Rita Pires
A folded symplectic form on a manifold is a closed 2-form with the mildest possible degeneracy along a hypersurface. A special class of folded symplectic manifolds are the origami…
Moduli spaces of toric manifolds
Álvaro Pelayo, Ana Rita Pires, Tudor S. Ratiu +1
We construct a distance on the moduli space of symplectic toric manifolds of dimension four. Then we study some basic topological properties of this space, in particular, path-conn…
Symplectic and Poisson geometry on b-manifolds
Victor Guillemin, Eva Miranda, Ana Rita Pires
Let be a Poisson manifold with Poisson bivector field . We say that is b-Poisson if the map intersects the zero section transversally on a codi…
Codimension one symplectic foliations and regular Poisson structures
Victor Guillemin, Eva Miranda, Ana Rita Pires
In this short note we give a complete characterization of a certain class of compact corank one Poisson manifolds, those equipped with a closed one-form defining the symplectic fol…
Symplectic Origami
A. Cannas da Silva, V. Guillemin, A. R. Pires
An origami manifold is a manifold equipped with a closed 2-form which is symplectic except on a hypersurface where it is like the pullback of a symplectic form by a folding map and…