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#Computational Topology

Showing: 29 courses
Applied Algebraic Topology Network

Computable Stability for Persistence Rank Function Machine Learning

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Exploring persistent rank functions and rank invariants as alternatives to persistent homology barcodes, with applications in machine learning and topological data analysis.
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1 Lesons
57 minutes
On-Demand
Free-Video
Banach Center

Perception of Visual Art and Topological Data Analysis

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Explore the intersection of visual art perception and topological data analysis, uncovering new insights into artistic interpretation and mathematical techniques.
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1 Lesons
45 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Geometry and Topology of Periodic Point Sets, for Example Crystals

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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.
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25 Lesons
53 minutes
On-Demand
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

Barcodes for the Topological Analysis of Gradient-Like Vector Fields

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Explore topological analysis of gradient-like vector fields using barcodes. Learn about chain complexes, parametrization, and applications in smooth and discrete settings, with insights on stability and approximation.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Embeddings and Tverberg-Type Problems: New Algorithms and Undecidability Results

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Explore computational topology: algorithmic embeddability, undecidability in higher dimensions, and polynomial-time decidability of r-Tverberg problem in metastable range.
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8 Lesons
26 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Pawel Dlotko - A Few Simple Stories on Topology in Action

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Explore practical applications of computational topology in material science, dynamical systems, and brain research. Learn how theory and algorithms work together to solve real-world problems.
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20 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Bradley Nelson: Parameterized Vietoris-Rips Filtrations via Covers

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Explore computational topology techniques for large filtered geometric complexes, focusing on Vietoris-Rips filtrations and cover-based methods for parallel computation and compression.
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15 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Persistence-Based Skeletonization of Images

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Explores algorithms for splitting images into convex polygons using topological persistence, including Convex Constrained Mesh and Persistent Resolution-Independent Mesh for edge detection.
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1 Lesons
30 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Every Stable Invariant of Finite Metric Spaces Produces False Positives

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Explore stable invariants in computational topology, their limitations in approximating Gromov-Hausdorff distance, and the inevitability of false positives when using Hilbert space-valued invariants.
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1 Lesons
56 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Multiscale Many-body Correlations and Structure in Chemistry Data

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Integrating graphs, topology, and geometry to analyze complex chemistry data, providing insights into multiscale correlations and structures beyond traditional methods.
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1 Lesons
50 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Wasserstein Distances, Geodesics and Barycenters of Merge Trees

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Explore computational frameworks for merge trees, including Wasserstein distances, geodesics, and barycenters. Learn efficient algorithms and applications in visualization, feature tracking, and ensemble clustering.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Javier Arsuaga - Applications of Computational Topology to the Analysis of Breast Cancer

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Explore computational topology's role in breast cancer analysis, uncovering new insights through advanced mathematical techniques and data visualization methods.
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1 Lesons
59 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Scalable Computation of the Extremum Graph

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Explore scalable computation of extremum graphs, a simplified topological descriptor for scalar functions, with applications in visualization and shape analysis. Learn efficient parallel algorithms for large datasets.
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1 Lesons
48 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Demystifying Latschev's Theorem for Manifold Reconstruction

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Explores quantitative approaches to Latschev's theorem for topological manifold reconstruction, advancing finite sample analysis in data science and manifold learning applications.
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1 Lesons
49 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Classical Topology and Quantum Complexity - IPAM at UCLA

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Explore the intersection of classical topology and quantum complexity, focusing on computational challenges in determining homology groups and their implications for quantum mechanics and data analysis.
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1 Lesons
54 minutes
On-Demand
Free-Video
MUNI Seminar Series

Topological Perspectives on Networks

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Explore algebraic topology tools for network analysis, focusing on their application in neuroscience to understand structure-function relationships.
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1 Lesons
53 minutes
On-Demand
Free-Video
MUNI Seminar Series

Topological Perspectives on Networks

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Explore algebraic topology tools for network analysis, focusing on their application in neuroscience to understand structure-function relationships.
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1 Lesons
53 minutes
On-Demand
Free-Video
SAIConference

Understanding Complex Biological Systems: A Journey into Computational Topology

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Explore computational topology's role in decoding complex biological systems. Learn how algorithms interpret data from molecular biology, genetics, and medicine, offering unique insights into disease progression and protein structures.
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11 Lesons
33 minutes
On-Demand
Free-Video
Institut Henri Poincaré

The Genus-One Question for Open Book Decomposition in Contact Structures and Anosov Flows

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Explore the genus-one question for open book decomposition in 3D contact structures and Anosov flows, examining constructions and partial results.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Geometrization and its Consequences in 3-Manifold Topology - Part I

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Explore Thurston's geometric perspective on 3-manifolds, including Perelman's Geometrization Theorem, and its implications for topology, algorithms, and group theory in 3-dimensional spaces.
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1 Lesons
58 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Geometrization and Its Consequences in 3-Manifold Topology - Part II

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Explore Thurston's geometric perspective on 3-manifolds, Perelman's Geometrization Theorem, and their impact on topology. Discover algorithmic and group-theoretic applications in 3-manifold theory.
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1 Lesons
59 minutes
On-Demand
Free-Video
BIMSA

Polynomial Bounds on Reidemeister Moves in Knot Theory

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Explore polynomial bounds on Reidemeister moves in knot theory, examining algorithms for trivial knot recognition and the relationship between diagram complexity and move sequences.
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1 Lesons
50 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Geometrization and its Consequences in 3-Manifold Topology - Lecture 4

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Explore hyperbolic geometry's role in 3-manifold topology, including Thurston's viewpoint and Perelman's theorem. Discover algorithmic and group-theoretic applications in computational experiments.
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1 Lesons
59 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Geometrization and its Consequences in 3-Manifold Topology - Lecture 3

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Explore Thurston's geometric perspective on 3-manifolds, Perelman's Geometrization Theorem, and their impact on topology, algorithms, and group theory in 3D geometry.
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1 Lesons
55 minutes
On-Demand
Free-Video
Squid: Schools for Quantum Information Development

Gapped Clique Homology is QMA1-Hard and Contained in QMA

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Explore the complexity of homology problems in computational topology, focusing on clique complexes and their quantum complexity classification through innovative eigenvalue analysis techniques.
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1 Lesons
24 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Dimensionality Reduction via Distributed Persistence - DIPOLE

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Explore dimensionality reduction with DIPOLE, a novel approach combining local metric and global topological preservation for improved data visualization and analysis.
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13 Lesons
59 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Measuring Graph Distance Using the Labeled Merge Tree Interleaving Distance

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Explore geometric graph analysis through merge trees, learning advanced techniques for measuring distances between networks using directional transforms and multi-labeling schemes.
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1 Lesons
48 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Computing Generalized Ranks of Persistence Modules via Unfolding to Zigzag Modules

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Efficient algorithm for computing generalized ranks of persistence modules using unfolding to zigzag modules, with applications in algebraic topology and data analysis.
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1 Lesons
46 minutes
On-Demand
Free-Video