An introduction to multiparameter persistence
In topological data analysis (TDA), one often studies the shape of data by constructing a
filtered topological space, whose structure is then examined using persistent homology …
filtered topological space, whose structure is then examined using persistent homology …
Toward a spectral theory of cellular sheaves
This paper outlines a program in what one might call spectral sheaf theory—an extension of
spectral graph theory to cellular sheaves. By lifting the combinatorial graph Laplacian to the …
spectral graph theory to cellular sheaves. By lifting the combinatorial graph Laplacian to the …
Homological algebra of modules over posets
E Miller - arXiv preprint arXiv:2008.00063, 2020 - arxiv.org
Homological algebra of modules over posets is developed, as closely parallel as possible to
that of finitely generated modules over noetherian commutative rings, in the direction of finite …
that of finitely generated modules over noetherian commutative rings, in the direction of finite …
Homological algebra for persistence modules
P Bubenik, N Milićević - Foundations of Computational Mathematics, 2021 - Springer
We develop some aspects of the homological algebra of persistence modules, in both the
one-parameter and multi-parameter settings, considered as either sheaves or graded …
one-parameter and multi-parameter settings, considered as either sheaves or graded …
Euler characteristic surfaces
G Beltramo, R Andreeva, Y Giarratano… - arXiv preprint arXiv …, 2021 - arxiv.org
We study the use of the Euler characteristic for multiparameter topological data analysis.
Euler characteristic is a classical, well-understood topological invariant that has appeared in …
Euler characteristic is a classical, well-understood topological invariant that has appeared in …
Weighted persistent homology
In this paper, we develop the theory of weighted persistent homology. In 1990, Dawson [9]
was the first to study in depth the homology of weighted simplicial complexes. We generalize …
was the first to study in depth the homology of weighted simplicial complexes. We generalize …
On the Hochschild cohomology of Tamarkin categories
arXiv:2312.11447v1 [math.SG] 18 Dec 2023 On the Hochschild cohomology of Tamarkin
categories Page 1 arXiv:2312.11447v1 [math.SG] 18 Dec 2023 On the Hochschild cohomology …
categories Page 1 arXiv:2312.11447v1 [math.SG] 18 Dec 2023 On the Hochschild cohomology …
Barcodes and area-preserving homeomorphisms
F Le Roux, S Seyfaddini, C Viterbo - Geometry & Topology, 2021 - msp.org
We use the theory of barcodes as a new tool for studying dynamics of area-preserving
homeomorphisms. We will show that the barcode of a Hamiltonian diffeomorphism of a …
homeomorphisms. We will show that the barcode of a Hamiltonian diffeomorphism of a …
Data structures for real multiparameter persistence modules
E Miller - arXiv preprint arXiv:1709.08155, 2017 - arxiv.org
A theory of modules over posets is developed to define computationally feasible,
topologically interpretable data structures, in terms of birth and death of homology classes …
topologically interpretable data structures, in terms of birth and death of homology classes …
Sheaves and symplectic geometry of cotangent bundles
S Guillermou - Astérisque, 2023 - inria.hal.science
This paper is essentially made of the three preprints arXiv: 1212.5818, arXiv: 1311.0187,
arXiv: 1603.07876 gathered in a single text, with simplified proofs. We recall several results …
arXiv: 1603.07876 gathered in a single text, with simplified proofs. We recall several results …