Courant, Bezout, and Persistence - Lecture 2
Explore spectral geometry through persistence modules and barcodes, examining oscillation of functions and applications to Courant's nodal domain theorem and Bezout's theorem in eigenfunctions.
Courant, Bezout, and Persistence in Spectral Geometry - Lecture 1
Explore spectral geometry and topological persistence, focusing on oscillation of functions, Courant's nodal domain theorem, and Bezout's theorem in the context of eigenfunctions.
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.
Computing Persistent Homology - Introduction
Explore the fundamentals of persistent homology computation, covering key concepts, intuition, and practical applications in topological data analysis.
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.
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.
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.
Vanessa Robins - The Extended Persistent Homology Transform for Manifolds with Boundary
Explore extended persistent homology transform for shape analysis, offering finite distances between shapes with different Betti numbers and applications in shape clustering.
Saecular Persistence
Explore saecular persistence, a method to decompose persistence modules with non-field coefficients. Learn about applications in topology, generalized persistence diagrams, and scientific data analysis.
Homological Algebra for Persistence Modules
Introduction to persistence modules in algebraic topology, exploring tensor products, Hom operations, and their role in homological algebra. Insights into preserving exact sequences and advanced concepts.
Extracting Persistence Features with Hierarchical Stabilisation
Explore hierarchical stabilisation for extracting stable invariants from persistence modules, focusing on the stable rank and its applications in data analysis and classification tasks.
On the Algebraic Geometry of Spaces of Persistence Modules
Explore algebraic geometry's application to persistence modules in topological data analysis, offering insights into data structure and shape analysis.
On the Hofer-Zehnder Conjecture - Periodic Points of Hamiltonian Diffeomorphisms
Explore Hofer-Zehnder conjecture on periodic points of Hamiltonian diffeomorphisms, examining recent progress using persistence modules, barcodes, and Floer cohomology power operations.
Generalized Persistence Algorithm for Decomposing Multi-Parameter Persistence Modules
Explore a generalized persistence algorithm for decomposing multi-parameter persistence modules, enhancing topological data analysis with improved computational efficiency and structural insights.
Parallel Decomposition of Persistence Modules Through Interval Bases
Exploring parallel decomposition of persistence modules using interval bases, with applications in Topological Data Analysis and connections to the Hodge Laplacian.
Harder-Narasimhan Filtrations of Persistence Modules
Explore Harder-Narasimhan types in quiver representations, examining their applications and limitations in persistence modules across various contexts in algebraic topology.
Computing Generalized Ranks of Persistence Modules via Unfolding to Zigzag Modules
Efficient algorithm for computing generalized ranks of persistence modules using unfolding to zigzag modules, with applications in algebraic topology and data analysis.