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Applied Algebraic Topology

Free Online

Applied Algebraic Topology Courses and Certifications

Explore persistent homology, topological data analysis, and computational topology through expert interviews and technical seminars. Learn cutting-edge applications like cell complex neural networks and JavaPlex on YouTube, featuring pioneers like Gunnar Carlsson and Herbert Edelsbrunner discussing real-world implementations.

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Applied Algebraic Topology Network
Approximate and Discrete Vector Bundles

Explore synchronization problems and dimensionality reduction through vector bundles. Learn how characteristic classes provide insights into global synchronization and data analysis challenges.
- YouTube
- 1 hour
- Self-Paced
- Free Video
Applied Algebraic Topology Network
Gunnar Carlsson Interviewed by Vin de Silva - February 3, 2021

Insightful interview with Gunnar Carlsson, exploring topics in applied algebraic topology and its applications in data analysis and machine learning.
- YouTube
- 56 minutes
- Self-Paced
- Free Video
Applied Algebraic Topology Network
Universality of Persistence Diagrams and Bottleneck & Wasserstein Distances

Explore the mathematical foundations of persistence diagrams and their associated metrics, focusing on universality properties and distance calculations in topological data analysis.
- YouTube
- 28 minutes
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- Free Video
Applied Algebraic Topology Network
Efficient Approximation of the Matching Distance for 2-Parameter Persistence

Explore efficient algorithms for approximating matching distance in 2-parameter persistence modules, focusing on quad-tree refinement and local adaptive bounds for improved computational performance.
- YouTube
- 30 minutes
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- Free Video
Applied Algebraic Topology Network
Solving Equations and Optimization Problems with Uncertainty

Explore algorithms for detecting zeros of imprecise continuous functions and approximating worst-case optima in optimization problems with uncertain feasible domains.
- YouTube
- 43 minutes
- Self-Paced
- Free Video
Applied Algebraic Topology Network
Stratified Covering Maps and Interleavings

Explore stratified covering maps and interleavings in algebraic topology, examining their applications and theoretical foundations.
- YouTube
- 59 minutes
- Self-Paced
- Free Video
Applied Algebraic Topology Network
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.
- YouTube
- 54 minutes
- Self-Paced
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Applied Algebraic Topology Network
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.
- YouTube
- 31 minutes
- Self-Paced
- Free Video
Applied Algebraic Topology Network
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.
- YouTube
- 26 minutes
- Self-Paced
- Free Video
Applied Algebraic Topology Network
Takashi Owada - Limit Theorems for Topological Invariants of the Dynamic Multi-Parameter Simplicial Complex

Explore topological invariants in dynamic multi-parameter simplicial complexes, covering connectivity, probability, and limiting processes in applied algebraic topology.
- YouTube
- 28 minutes
- Self-Paced
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Applied Algebraic Topology Network
Vanessa Robins Interviewed by Elizabeth Bradley

Explore applied topology with Vanessa Robins as she discusses her career journey, research interests, and insights on granular materials, collaborations, and emerging areas in the field.
- YouTube
- 50 minutes
- Self-Paced
- Free Video
Applied Algebraic Topology Network
Tamal Dey - A Framework for Topological Summarization

Explore topological summarization frameworks, covering concepts like nerve complexes, multiscale mapper, persistence diagrams, and stability in hierarchical covers. Gain insights into advanced computational topology techniques.
- YouTube
- 57 minutes
- Self-Paced
- Free Video
Applied Algebraic Topology Network
Omer Bobrowski - Maximally Persistent Cycles in Random Geometric Complexes

Explore persistent cycles in random geometric complexes, examining key tools, processes, and results. Gain insights into random graph theory and future research directions.
- YouTube
- 1 hour
- Self-Paced
- Free Video
Applied Algebraic Topology Network
Benjamin Schweinhart - Statistical Topology of Random Cell Complexes, and Applications

Explore statistical topology of random cell complexes, covering curvature flow, grain growth, graph limits, and computational evidence for steady state hypothesis.
- YouTube
- 59 minutes
- Self-Paced
- Free Video
Applied Algebraic Topology Network
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.
- YouTube
- 55 minutes
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