Applied Algebraic Topology Network Courses

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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• Free Video

Applied Topology for Discrete Structures

Explore topological concepts applied to discrete structures modeling real data, bridging network science and applied topology for innovative analysis of complex systems.

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

The Reeb Graph of a Smooth Function Encodes the Function Class and Manifold Type

Explore how Reeb graphs of smooth functions encode function class and manifold type, examining structures for Morse and Morse-Bott functions and their relationship to manifold properties.

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

Topological Time Series Analysis for Hurricanes and Dynamical Systems

Explore topological data analysis applications in studying hurricane satellite imagery and dynamical system bifurcations using persistent homology and zigzag persistence techniques.

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

Urs Lang - Combinatorial Dimension and Higher-Rank Hyperbolicity

Exploration of (n,δ)-hyperbolicity in metric spaces, its relation to Gromov's δ-hyperbolicity, and applications in geometric group theory and hierarchically hyperbolic groups.

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