2 citations · 2 across the 7 of their papers we have counts for
7 papers
Data-Driven Diffusion Processes on Differential Forms via the Projected Ambient Connection Laplacian
Alvaro Almeida Gomez, Jorge Duque Franco
We develop a data-driven approximation of the projected ambient connection Laplacian acting on differential forms over smooth Riemannian manifolds sampled by point clouds. The prop…
Automorphism groups of rigid complete intersections
Jorge Duque Franco, Alvaro Liendo, Ana Julisa Palomino
We study the automorphism groups of complete intersections of hypersurfaces of strictly increasing degrees in projective space. Under a combinatorial rigidity condition on the tupl…
Hodge Laplacians and Hodge Diffusion Maps
Alvaro Almeida Gomez, Jorge Duque Franco
We introduce Hodge Diffusion Maps, a novel manifold learning algorithm designed to analyze and extract topological information from high-dimensional data-sets. This method approxim…
On the Picard number and the extension degree of period matrices of complex tori
Robert Auffarth, Jorge Duque Franco
The rank of the Néron-Severi group of a complex torus of dimension satisfies The degree of the extension field generated over $…
Periods of join algebraic cycles
Jorge Duque Franco, Roberto Villaflor Loyola
We show, for all even and , that the moduli of smooth degree hypersurfaces of contains infinitely many different Hodge loci whos…
On fake linear cycles inside Fermat varieties
Jorge Duque Franco, Roberto Villaflor Loyola
We introduce a new class of Hodge cycles with non-reduced associated Hodge loci, we call them fake linear cycles. We characterize them for all Fermat varieties and show that they e…
Periods of Hodge cycles and special values of the Gauss' hypergeometric function
Jorge Duque Franco
We compute periods of perturbations of a Fermat variety. This allows us to consider a subspace of the Hodge cycles defined by "simple" arithmetic conditions. We explore some exampl…