Sampling Smooth Manifolds Using Ellipsoids
Explore sampling smooth manifolds using ellipsoids, a novel approach requiring lower sample density than traditional ball-based methods, with potential applications in data science and topology.
Detecting Bifurcations in Dynamical Systems with Zigzag Persistent Homology
Explore zigzag persistent homology for efficient detection of bifurcations in dynamical systems, reducing computational costs and capturing topological changes in a single persistence diagram.
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.
Computing Persistent Homology - Introduction
Explore the fundamentals of persistent homology computation, covering key concepts, intuition, and practical applications in topological data analysis.
Geometric and Topological Data Analysis of Enzyme Kinetics
Explore geometric and topological data analysis techniques applied to enzyme kinetics, focusing on ERK molecular dynamics and its implications for cancer and developmental defects.
Conley-Morse-Forman Theory for Generalized Combinatorial Multivector Fields
Generalized combinatorial multivector fields on finite topological spaces: extending Conley-Morse-Forman theory for data science applications, including isolated invariant sets, Conley index, and Morse decompositions.
Ronen Eldan- Revealing the Simplicity of High-Dimensional Objects via Pathwise Analysis
Explore high-dimensional geometry through pathwise analysis, revealing simple structures in complex spaces and their applications in probability theory and statistical physics.
Ulrich Bauer - Persistence Diagrams as Diagrams
Explore persistence diagrams as categorical functors, examining their structure, stability, and relationships to matchings. Learn about new constructions and theorems in this advanced algebraic topology lecture.
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.
Nonlinear Dynamics, High Dimensional Data, and Persistent Homology
Explore nonlinear dynamics, high-dimensional data analysis, and persistent homology with Konstantin Mischaikow. Learn about algebraic topology applications, persistence diagrams, and recent advancements in data science.
Gunnar Carlsson - Local to Global Principles in Persistent Homology
Explore persistent homology's local-to-global principles, computational methods, and applications in topology and data analysis with expert Gunnar Carlsson.
From Persistent Homology to Machine Learning
Overview of persistent homology's applications in machine learning, exploring its use in analyzing global topology and local geometry of datasets, with examples from various fields and discussions on stability and interpretability.
Invariants for Tame Parametrised Chain Complexes
Explore invariants for tame parametrised chain complexes in applied algebraic topology, focusing on explicit constructions, comprehensive frameworks, and discriminative power in topological data analysis.
Lower Dimensional Topological Information: Theory and Applications
Explore lower dimensional topological features in data analysis, covering detection methods, theoretical foundations, and applications in image segmentation using topological and statistical approaches.
Why Should Q=P in the Wasserstein Distance Between Persistence Diagrams?
Explore Wasserstein distance in persistence diagrams, focusing on q=p choice. Covers geometric implications, stability results, algebraic versions, and computational advantages for central tendencies.
Geometric Interpretation of Persistence
Explore geometric interpretations of persistence in algebraic topology, covering space reconstruction, one-dimensional persistent homology classification, and detection of contractible geodesics using higher-dimensional features.
Limit Theorems in Topological Data Analysis
Explore limit theorems in topological data analysis, focusing on barcodes, persistence modules, and random persistence modules. Learn about convergence proofs and expectations for uniform distributions on compact submanifolds.
Persistence in Functional Topology
Explore functional topology's evolution, connecting persistent homology to critical point theory and calculus of variations. Gain insights into Morse's theory and its application to minimal surfaces.
Conversation on the Paper "Persistent Extension and Analogous Bars" by Yoon, Ghrist, Giusti
Explore persistent homology extensions and analogous bars in topological data analysis, discussing novel methods for comparing persistence barcodes and their applications in data science.
Geometry and Topology of Periodic Point Sets, for Example Crystals
Explore geometric and topological tools for characterizing crystalline materials, including Brillouin zones and persistent homology, and discuss challenges in defining persistent homology for periodic point sets.
Henry Adams - Vietoris-Rips Complexes of Hypercube Graphs
Explore Vietoris-Rips complexes of hypercube graphs, their homotopy types, and applications in genetic recombination and persistent homology. Discover formulas, open questions, and conjectures in this fascinating area of applied algebraic topology.