Applied Algebraic Topology Network Courses

Quantum Topological Data Analysis - Part 1

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Explore quantum persistent homology algorithms for pattern recognition in data, leveraging quantum computing's potential to enhance traditional Topological Data Analysis methods and improve efficiency.

• YouTube
• 26 minutes
• On-Demand
• Free Video

Scalable Computation of the Extremum Graph

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.

• YouTube
• 48 minutes
• On-Demand
• Free Video

Using Topology to Study the Geometry of Neural Correlations

Explore how topology and persistent homology uncover hidden structures in neural data, focusing on Betti curves and their applications in analyzing hippocampal, olfactory, and zebrafish brain activity.

• YouTube
• 1 hour 8 minutes
• On-Demand
• Free Video

TDA for Chromatic Point Clouds

Generalizace persistentní homologie pro barevné bodové mraky. Detekce prostorových interakcí mezi různými typy bodů s aplikacemi v biologii a medicíně.

• YouTube
• 58 minutes
• On-Demand
• Free Video

Demystifying Latschev's Theorem for Manifold Reconstruction

Explores quantitative approaches to Latschev's theorem for topological manifold reconstruction, advancing finite sample analysis in data science and manifold learning applications.

• YouTube
• 49 minutes
• On-Demand
• Free Video

Bi-Lipschitz Embeddings of the Space of Persistence Barcodes

Explore bi-Lipschitz embeddings of persistence barcodes into Hilbert space, focusing on Figalli and Gigli's metric for optimal partial transport and its applications to unordered m-tuples.

• YouTube
• 31 minutes
• On-Demand
• Free Video

Reconstructing Hidden Geometric Structures in Data From Distance Matrices

Explore techniques for reconstructing metric spaces and embeddings from distance matrices, covering theoretical foundations, practical applications, and open problems in geometric data analysis.

• YouTube
• 1 hour 1 minute
• On-Demand
• Free Video

Stabilizing Decomposition of Multiparameter Modules

Explores stability theories for multiparameter module decomposition, addressing challenges and presenting recent findings. Discusses potential strengthening of stability results for staircase decomposable modules.

• YouTube
• 46 minutes
• On-Demand
• Free Video

Urysohn Width

Explore the 100-year history and applications of Urysohn width, a metric invariant quantifying space approximation by simplicial complexes. Discover its role in dimension theory and modern geometric challenges.

• YouTube
• 54 minutes
• On-Demand
• Free Video

Topology in Digital Sound Synthesis

Exploring topological concepts in digital sound synthesis, from oscillatory algorithms to wave equations and filter theory, with applications in computational audio generation.

• YouTube
• 54 minutes
• On-Demand
• Free Video

Ordering Descriptor Types by Their Ability to Faithfully Represent Shapes

Explore topological descriptors in shape comparison, focusing on augmented vs non-augmented types and their ability to faithfully represent simplicial complexes. Accessible discussion with interesting open questions and visuals.

• YouTube
• 47 minutes
• On-Demand
• Free Video

Exploiting Geometric Structure in Matrix-Valued Optimization

Exploring optimization on matrix manifolds, introducing Riemannian Frank-Wolfe methods for constrained problems, and discussing applications in machine learning and mathematics.

• YouTube
• 58 minutes
• On-Demand
• Free Video

An Upper Bound on the Sequential Topological Complexity

Exploring upper bounds on sequential topological complexity in robot motion planning, with applications to lens spaces and improved dimensional upper bounds under group actions.

• YouTube
• 47 minutes
• On-Demand
• Free Video

Michael Bronstein: Physics-Inspired Graph Neural Networks

Explore physics-inspired continuous learning models for graph neural networks, leveraging tools from differential geometry and algebraic topology to enhance expressive power beyond traditional message-passing paradigms.

• YouTube
• 1 hour 2 minutes
• On-Demand
• Free Video

Julien Tierny - Principal Geodesic Analysis of Merge Trees and Persistence Diagrams

Computational framework for Principal Geodesic Analysis of merge trees, adapting PCA to Wasserstein metric space. Efficient algorithm for data reduction and dimensionality reduction in topological data analysis.

• YouTube
• 55 minutes
• On-Demand
• Free Video