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#Vietoris-Rips Complexes

Showing: 17 courses
Applied Algebraic Topology Network

Henry Adams - Vietoris-Rips Complexes of Hypercube Graphs

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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.
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13 Lesons
45 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Star Clusters in Clique Complexes and the Vietoris-Rips Complex of Planar Sets

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Explore star clusters in simplicial complexes and their applications to independence complexes and Vietoris-Rips complexes of planar sets, with insights on homotopy information and related conjectures.
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11 Lesons
50 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Vietoris-Rips Complexes of Hypercube Graphs

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Explore Vietoris-Rips complexes of hypercube graphs, their collapsibility, and applications in genetic trees and persistent homology. Gain insights into simplicial complexes and topological data analysis.
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8 Lesons
34 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Homotopical Decompositions of Simplicial and Vietoris Rips Complexes

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Explore homotopical decompositions of simplicial complexes, focusing on obstruction complexes and their applications in topological data analysis, with insights on Vietoris-Rips complexes.
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1 Lesons
31 minutes
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Free-Video
Applied Algebraic Topology Network

The Vietoris Rips Complex of the Circle

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Explore the Vietoris-Rips complex of the circle, its homotopy types at different thresholds, and implications for persistent homology in topological data analysis.
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1 Lesons
57 minutes
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Free-Video
Applied Algebraic Topology Network

Bridging Applied and Quantitative Topology

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Survey of emerging connections between applied and quantitative topology, focusing on Vietoris-Rips complexes and their applications in computational topology, geometric group theory, and dataset shape approximation.
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1 Lesons
58 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Vietoris-Rips Persistent Homology, Injective Metric Spaces, and The Filling Radius

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Explore geometric persistent homology, its isomorphism with Vietoris-Rips filtration, and applications in characterizing persistence barcodes, bounding intervals, and connecting to filling radius.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Vietoris-Rips Thickenings - Problems for Birds and Frogs

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Explore open problems in Vietoris-Rips complexes, connecting diverse mathematical areas. Suitable for both broad theorists and problem-solving specialists in applied algebraic topology.
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1 Lesons
1 hour 18 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Decomposing Simplicial Complexes - Without Losing Pieces

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Explore simplicial complex decomposition, its impact on homotopy type, and applications in Vietoris-Rips complexes. Learn about obstruction complexes and their role in understanding topological changes.
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9 Lesons
48 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Andrew Thomas - Functional Limit Theorems for Euler Characteristic Processes

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Explore functional limit theorems for Euler characteristic processes in Vietoris-Rips complexes, covering strong law of large numbers and central limit theorem in the thermodynamic regime.
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18 Lesons
59 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Johnathan Bush - Maps of Čech and Vietoris–Rips Complexes into Euclidean Spaces

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Explore simplex-preserving maps in Čech and Vietoris–Rips complexes, their applications, and the challenge of finding such maps from various domains to Euclidean spaces.
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11 Lesons
45 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Ulrich Bauer - Gromov Hyperbolicity, Geodesic Defect, and Apparent Pairs in Rips Filtrations

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Explore Gromov hyperbolicity, geodesic defect, and apparent pairs in Rips filtrations, extending Rips' results on contractibility and examining computational implications for persistent homology.
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12 Lesons
54 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Vietoris-Rips Complexes and Geometric Group Theory

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Explore Vietoris-Rips complexes in geometric group theory, focusing on topological finiteness properties, hyperbolic groups, and recent developments in Morse theory and persistent homology.
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1 Lesons
51 minutes
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Free-Video
Applied Algebraic Topology Network

Homotopy Types of Vietoris–Rips Complexes of Metric Gluings

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Explore homotopy types of Vietoris-Rips complexes in metric wedge sums and gluings, with applications to persistent homology of metric graphs and insights into open research directions.
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1 Lesons
1 hour 11 minutes
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Free-Video
Applied Algebraic Topology Network

A Counter-Example to Hausmann's Conjecture

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Explore a counter-example to Hausmann's conjecture on Vietoris-Rips complexes, challenging long-held beliefs in algebraic topology using persistent homology.
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1 Lesons
53 minutes
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Free-Video
Applied Algebraic Topology Network

Gromov-Hausdorff Distances, Borsuk-Ulam Theorems, and Vietoris-Rips Complexes

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Explore Gromov-Hausdorff distances, Borsuk-Ulam theorems, and Vietoris-Rips complexes in geometry. Learn about recent advancements in lower bounding distances between spheres using innovative mathematical techniques.
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1 Lesons
57 minutes
On-Demand
Free-Video
Fields Institute

Some Remarks on the Cohomology of the Vietoris-Rips Complex of a Hypercube Graph

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Explore advanced algebraic topology concepts, focusing on the cohomology of Vietoris-Rips complexes in hypercube graphs, with insights from expert Martin Bendersky.
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1 Lesons
47 minutes
On-Demand
Free-Video