Applied Algebraic Topology Network Courses

Hubert Wagner - Topological Data Analysis in Non-Euclidean Spaces

Explore topological data analysis in non-Euclidean spaces, focusing on techniques for applying TDA tools and their applications in detecting neural network backdoor attacks.

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

Topological Uncertainty and Representations for Biomedical Image Analysis

Innovative approach to biomedical image analysis using topological structures and uncertainty, enhancing segmentation accuracy and enabling interactive annotation for fine-scale delineation.

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

Bounds for the Higher Topological Complexity of Configuration Spaces

Explore bounds for higher topological complexities in unordered configuration spaces of trees and anchored configuration spaces of circles with two anchor points.

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

Topological Methods in Discrete Geometry

Explore topological applications in discrete geometry, focusing on mass partitions and Helly-type theorems. Learn about classical results and recent generalizations in these areas.

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

Exact Multi-Parameter Persistent Homology of Time-Series Data

Explore multi-parameter persistent homology for time-series data analysis, featuring an exact formula for one-dimensional reduction and efficient computational methods using Fourier decomposition and Liouville torus.

• 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

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

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

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

Reconstructing Manifolds by Weighted L_1-Norm Minimization

Innovative approach to shape reconstruction using weighted l_1-norm minimization, transforming triangulation into a convex optimization problem for smooth orientable manifolds in high-dimensional spaces.

• YouTube
• 51 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

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

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

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

José Samper Seminar - Higher Chordality

Explore higher chordality in algebraic topology, covering community algebra, linear resolution, graphs, polytopes, and complex links. Gain insights into advanced mathematical concepts.

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