Applied Algebraic Topology Network Courses

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
• Self-Paced
• Free Video

Strange Random Topology of the Circle

Explore the intriguing behavior of "topological noise" in random Cech complexes constructed from the circle, revealing unexpected homotopy equivalences and higher Betti numbers in specific filtration radii intervals.

• YouTube
• 39 minutes
• Self-Paced
• Free Video

Triangulated Persistence Categories and Their K-Theory

Explore triangulated persistence categories, combining triangulated category theory and persistence modules. Learn about associated measurements, invariants, and K-theory, with examples from algebra and symplectic topology.

• YouTube
• 55 minutes
• Self-Paced
• 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
• Self-Paced
• 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
• Self-Paced
• Free Video

Higher Topological Complexity of a Map

Explore higher topological complexity of maps, extending Farber's concept. Learn about unified TC_{r,s}(f) and its relevance in r-multitasking motion planning for robot devices with s prescribed stages.

• YouTube
• 1 hour
• Self-Paced
• Free Video

Topology of Surprisal - Information Theory and Vietoris-Rips Filtrations

Explore the fusion of information theory and Vietoris-Rips filtrations, focusing on Kullback-Leibler divergence and its applications in deep learning, with insights on overcoming non-symmetry challenges.

• YouTube
• 59 minutes
• Self-Paced
• Free Video

Persistent Topological Laplacians

Explores persistent topological Laplacians to address limitations in topological data analysis, enhancing the handling of complex data and uncovering SARS-CoV-2 evolution mechanisms.

• YouTube
• 1 hour
• Self-Paced
• Free Video

Probabilistic Generative Frameworks for Sampling 3D Complex Shapes and Images

Explore probabilistic frameworks for simulating 2D and 3D shapes, with applications in computational biology. Learn about sub-image selection and shape statistics in cellular imaging and primate mandibular molars.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Topology of Artificial Neuron Activations in Deep Learning

Explore the topology of artificial neuron activations in deep learning, from image classification to natural language processing, with insights on convolutional neural networks and transformer-based models.

• YouTube
• 1 hour 3 minutes
• Self-Paced
• Free Video

Two Methods of Efficiently Approximating Semi-Algebraic Sets Up to Homotopy

Explores efficient methods for approximating semi-algebraic sets, focusing on singly exponential complexity algorithms and their applications in algebraic geometry.

• YouTube
• 1 hour
• Self-Paced
• Free Video

Antonio Rieser - Algebraic Topology for Graphs and Mesoscopic Spaces

Explore algebraic topology for graphs and mesoscopic spaces, covering homotopy, homology, and metric cohomology. Learn about pseudotopological spaces and their applications in various mathematical categories.

• YouTube
• 54 minutes
• Self-Paced
• Free Video

Small Density Vacuum and How to Find Them Robustly

Explore a new TDA method for identifying small density vacuums in high-density regions, with proven robustness and bounded persistence. Includes simulations and theoretical insights.

• YouTube
• 30 minutes
• Self-Paced
• Free Video

Every Stable Invariant of Finite Metric Spaces Produces False Positives

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.

• YouTube
• 56 minutes
• Self-Paced
• Free Video

Wanted- Topologists for Autonomous Robots Community

Exploring topological complexity in robotics: from path planning to task spaces. Insights into rigorous formulations for robotic autonomy, emphasizing environment topology and combinatorics in cooperative motion.

• YouTube
• 1 hour 5 minutes
• Self-Paced
• Free Video