4 papers
Cross effects for functors from posets
Bjørnar Gullikstad Hem
We establish a precise relationship between functor calculus and the projective dimension of multipersistence modules. Specifically, we develop a new notion of functor calculus for…
Decomposing multipersistence modules using functor calculus
Bjørnar Gullikstad Hem
We apply poset cocalculus, a functor calculus framework for functors out of a poset, to study the problem of decomposing multipersistence modules into simpler components. We both p…
Poset functor cocalculus and applications to topological data analysis
Bjørnar Gullikstad Hem
We introduce a new flavor of functor cocalculus, called \emph{poset cocalculus}, as a tool for studying approximations in topological data analysis. Given a functor from a distribu…
The discrete flow category: structure and computation
Bjørnar Gullikstad Hem
In this article, we use concepts and methods from the theory of simplicial sets to study discrete Morse theory. We focus on the discrete flow category introduced by Vidit Nanda, an…