Optimal Topological Simplification of Surfaces
Algorithmes et résultats de complexité pour simplifier la topologie des surfaces de manière optimale, en utilisant des courbes et graphes les plus courts possible.
Alexander Wagner - Nonembeddability of Persistence Diagrams into Hilbert Spaces
Explore nonembeddability of persistence diagrams in Hilbert spaces, examining stability, metrics, and implications for machine learning applications in topological data analysis.
Vanessa Robins - Persistence Diagrams of Bead Packings
Exploring grain-scale mechanisms in granular crystallization using X-ray tomography and persistent homology, revealing key formation processes of tetrahedral and octahedral pores in spherical bead packings.
Massimo Ferri - Selection of Points in Persistence Diagrams
Explore point selection in persistence diagrams, including Kurlin's criterion and the Ziqqurat method, for noise reduction and improved data analysis in topological data analysis.
On Characterizing Rare Events in Persistent Homology
Explore rare events in persistent homology, focusing on indecomposables in multi-parameter settings. Learn about large deviation principles and laws of large numbers in topological data analysis.
Approximation of Compact Metric Spaces by Finite Samples
Explore topological data analysis through finite approximations of compact metric spaces, connecting Shape Theory and Persistence for robust feature extraction from noisy datasets.
Barbara Giunti - Average Complexity of Barcode Computation for Vietoris-Rips Filtrations
Explore algorithmic complexity of persistent homology in random Vietoris-Rips filtrations, focusing on boundary matrix fill-up and its implications for computational efficiency.
A Topological Study of the Space of Planar Pentagons
Exploring topology of planar pentagons as a model for molecular conformation spaces, using topological data analysis for dimensionality reduction and visualization.
Differential Calculus on Persistence Barcodes
Explore differential calculus on persistence barcodes, covering differentiability concepts, lifts to ordered barcodes, and applications in topological data analysis.
The Vietoris Rips Complex of the Circle
Explore the Vietoris-Rips complex of the circle, its homotopy types at different thresholds, and implications for persistent homology in topological data analysis.
Ippei Obayashi - Stable Volumes for Persistent Homology
Explore stable volumes in persistent homology: a novel method to identify robust topological structures in data, overcoming instability issues and revealing minimal building blocks.
Multi-Parameter Persistent Homology is Practical
Explore practical applications of multi-parameter persistent homology in topological data analysis, focusing on efficient algorithms for large datasets and recent computational advancements.
Parallel Decomposition of Persistence Modules Through Interval Bases
Explore parallel decomposition of persistence modules using interval bases, enhancing Topological Data Analysis with distributed computation and Hodge decomposition techniques.
The Persistence Mayer-Vietoris Spectral Sequence
Explore the persistent Mayer-Vietoris spectral sequence, its applications in parallelizing persistent homology computations, and its ability to provide locality-enriched persistence barcodes.
Novel Computational Perspectives of Persistence
Explore innovative computational approaches to persistence in algebraic topology, focusing on advanced techniques and their applications in data analysis and topological research.
Greg Malen - Collapsibility of Random Clique Complexes
Explore k-collapsibility in random clique complexes, examining dimensional faces, strong connectivity, and homology implications for topological data analysis.
Solving Systems of ODEs via Combinatorial Homological Algebra
Exploring efficient computation of homological representations in dynamical systems, with applications to differential equations and parameter space analysis.
Topological Complexity Using Arbitrary Covers
Explore topological complexity using arbitrary covers, focusing on sectional category, ANRs, and generalized concepts. Gain insights into advanced algebraic topology techniques and applications.
Data Complexes, Obstructions, Persistent Data Merging
Explore data complexes, topological obstructions in database JOIN operations, and persistence levels in data alignment. Learn about measure theory, homotopy, and homology in the context of data integration.
Luis Scoccola - Locally Persistent Categories & Metric Properties of Interleaving Distances
Explore locally persistent categories, metric properties of interleaving distances, and their applications in algebraic topology, including natural interleavings and weak equivalences.
Nathanael Cox - Effective Algorithms for Quotients of Semi-Algebraic Equivalence Relations
Explore efficient algorithms for computing quotients of semi-algebraic equivalence relations, focusing on complexity, tools, and key results in applied algebraic topology.