5 papers
Generating Special Triangulations with Transformers
Charles Arnal, Jacky H. T. Yip, François Charton +1
Triangulations, i.e., well-structured decompositions of geometric objects into triangle-like pieces, are central objects in many domains of mathematics and physics. In particular,…
Transforming Calabi-Yau Constructions: Generating New Calabi-Yau Manifolds with Transformers
Jacky H. T. Yip, Charles Arnal, François Charton +1
Fine, regular, and star triangulations (FRSTs) of four-dimensional reflexive polytopes give rise to toric varieties, within which generic anticanonical hypersurfaces yield smooth C…
The distance function to a finite set is a topological Morse function
Charles Arnal
In this short note, we show that the distance function to any finite set is a topological Morse function, regardless of whether is in general position.…
Wasserstein convergence of Čech persistence diagrams for samplings of submanifolds
Charles Arnal, David Cohen-Steiner, Vincent Divol
Čech Persistence diagrams (PDs) are topological descriptors routinely used to capture the geometry of complex datasets. They are commonly compared using the Wasserstein distances $…
Critical points of the distance function to a generic submanifold
Charles Arnal, David Cohen-Steiner, Vincent Divol
In general, the critical points of the distance function to a compact submanifold can be poorly behaved. In this article, we show…