9 citations · 16 across the 4 of their papers we have counts for
7 papers
Evasion paths by homotopy limits
Gunnar Carlsson, Benjamin Filippenko, Wyatt Mackey
The evasion paths problem asks when a dynamically changing space can be navigated: imagine guards are patrolling a region, for instance, and we need to stay outside their view. We…
Topological Deep Learning
Ephy R. Love, Benjamin Filippenko, Vasileios Maroulas +1
This work introduces the Topological CNN (TCNN), which encompasses several topologically defined convolutional methods. Manifolds with important relationships to the natural image…
The space of sections of a smooth function
Gunnar Carlsson, Benjamin Filippenko
Given a compact manifold with boundary and a submersion whose restriction to the boundary of has isolated critical points with distinct critical value…
Persistent homology of the sum metric
Gunnar Carlsson, Benjamin Filippenko
Given finite metric spaces and , we investigate the persistent homology of the Cartesian product equipped with the sum metric $…
A Polyfold Proof of the Arnold Conjecture
Benjamin Filippenko, Katrin Wehrheim
We give a detailed proof of the homological Arnold conjecture for nondegenerate periodic Hamiltonians on general closed symplectic manifolds via a direct Piunikhin-Salamon-Schw…
Counterexamples in Scale Calculus
Benjamin Filippenko, Zhengyi Zhou, Katrin Wehrheim
We construct counterexamples to classical calculus facts such as the Inverse and Implicit Function Theorems in Scale Calculus -- a generalization of Multivariable Calculus to infin…