7 citations · 17 across the 10 of their papers we have counts for
11 papers
Gromov-Hausdorff Distances Between Spheres: Asymptotics and Vietoris-Rips Coindex Bounds
Sunhyuk Lim, Facundo Mémoli, Qingsong Wang
For , let be the infimum of the scales at which the Vietoris-Rips simplicial complex of the unit round sphere , equipped with its geodesic met…
Balanced Bismut torsion-parallel fourfolds with constant holomorphic sectional curvature
Qingsong Wang, Fangyang Zheng
An old conjecture in non-Kähler geometry states that, if a compact Hermitian manifold has constant holomorphic sectional curvature, then the metric must be Kähler (when the constan…
Elucidating Flow Matching ODE Dynamics with Respect to Data Geometries and Denoisers
Zhengchao Wan, Qingsong Wang, Gal Mishne +1
Flow matching (FM) models extend ODE sampler based diffusion models into a general framework, significantly reducing sampling steps through learned vector fields. However, the theo…
Vietoris--Rips Contractibility for Dense Subsets of Finite-Dimensional Normed Spaces
Qingsong Wang, Ling Zhou
Let be a -dense subset of a finite-dimensional normed space , so every point of is at distance at most from some point of . We prove that the open Vietoris--Ri…
Extremal spherical polytopes and Borsuk's conjecture
Mikhail Katz, Facundo Mémoli, Qingsong Wang
We generate anti-self-polar polytopes via a numerical implementation of the gradient flow induced by the diameter functional on the space of all finite subsets of the sphere, and p…
Gromov-Hausdorff distances, Borsuk-Ulam theorems, and Vietoris-Rips complexes
Henry Adams, Johnathan Bush, Nate Clause +13
We explore emerging relationships between the Gromov--Hausdorff distance, Borsuk--Ulam theorems, and Vietoris--Rips simplicial complexes. The Gromov--Hausdorff distance between two…
Some results about the Tight Span of spheres
Sunhyuk Lim, Facundo Memoli, Zhengchao Wan +2
The smallest hyperconvex metric space containing a given metric space X is called the tight span of X. It is known that tight spans have many nice geometric and topological propert…
The Persistent Topology of Optimal Transport Based Metric Thickenings
Henry Adams, Facundo Mémoli, Michael Moy +1
A metric thickening of a given metric space is any metric space admitting an isometric embedding of . Thickenings have found use in applications of topology to data analysis…
Metric Graph Approximations of Geodesic Spaces
Facundo Memoli, Osman Berat Okutan, Qingsong Wang
We study the question of approximating a compact geodesic metric space by metric graphs satisfying a uniform upper bound on their first Betti number. We prove that, up to a suitabl…
Manifolds with positive orthogonal Ricci curvature
Lei Ni, Qingsong Wang, Fangyang Zheng
In this paper we study the class of compact Kähler manifolds with positive orthogonal Ricci curvature: . First we illustrate examples of Kähler manifolds with $Ric^\pe…
On Bismut Flat Manifolds
Qingsong Wang, Bo Yang, Fangyang Zheng
In this paper, we give a classification of all compact Hermitian manifolds with flat Bismut connection. We show that the torsion tensor of such a manifold must be parallel, thus th…