143 citations · 581 across the 51 of their papers we have counts for
6 papers · 1 filter
Excision in equivariant fibred G-theory
Gunnar Carlsson, Boris Goldfarb
This paper provides a generalization of excision theorems in controlled algebra in the context of equivariant G-theory with fibred control and families of bounded actions. It also…
Persistent and Zigzag Homology: A Matrix Factorization Viewpoint
Gunnar Carlsson, Anjan Dwaraknath, Bradley J. Nelson
Over the past two decades, topological data analysis has emerged as a field of applied mathematics with new applications and algorithmic developments appearing rapidly. Two fundame…
Metric Representations of Network Data
Santiago Segarra, Gunnar Carlsson, Facundo Memoli +1
Networks are structures that encode relationships between pairs of elements or nodes. However, there is no imposed connection between these relationships, i.e., the relationship be…
Atiyah-Segal Derived Completions for Equivariant Algebraic G-Theory and K-Theory
Gunnar Carlsson, Roy Joshua
In the mid 1980s, while working on establishing completion theorems for equivariant Algebraic K- Theory similar to the well-known Atiyah-Segal completion theorem for equivariant to…
A Topology Layer for Machine Learning
Rickard Brüel-Gabrielsson, Bradley J. Nelson, Anjan Dwaraknath +3
Topology applied to real world data using persistent homology has started to find applications within machine learning, including deep learning. We present a differentiable topolog…
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 $…