4 papers
Balanced Bismut torsion-parallel fourfold 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 const…
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…
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…
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…