Applied Algebraic Topology Network Courses

Diffeomorphic Interpolation for Persistence-Based Topological Optimization

Discover how diffeomorphic interpolation enhances topological optimization in data analysis, focusing on efficient methods for processing large-scale point clouds with improved gradient computation techniques.

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

New Methods in Diffusion Geometry - Applications in Topological Data Analysis

Explore advanced techniques in diffusion geometry, including Riemannian geometry applications, vector calculus, and spatial PDEs for robust data analysis and topological insights.

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

Vietoris-Rips Complex as a Graph Complex

Explore the fundamental concepts of Vietoris-Rips Complex and its relationship to graph theory, including neighborhood, clique, independence, and cut complexes in topological data analysis.

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

Working with Persistence Curves Using the Masspcf Python Package

Discover how to work with piecewise constant functions in Python using 'masspcf', focusing on persistent homology applications like Betti curves and Euler characteristic curves.

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

Topological Data Analysis for Correlation Matrices - Implementation and Structure Extraction

Explore practical implementations of topological data analysis for correlation matrices, including order complexes, null models, and PyCliqueTop_2023 tools for extracting meaningful structural patterns.

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

Categorification of Multiparameter Persistent Homology

Explore how category theory enhances understanding of multiparameter persistent homology, offering new perspectives for analyzing complex topological data structures.

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

Tools for Homotopy Computations in Simplicial Complexes from Graphs

Explore computational methods for determining homotopy types in independence complexes, with applications to clique and matching complexes in graph theory.

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

Simplicial Complex and Euler Characteristic - An Intuitive Introduction

Explore the fundamentals of simplicial complexes and Euler characteristic through intuitive geometric examples and visual demonstrations of topological concepts.

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

Covering Type in Applied Algebraic Topology

Explore fundamental concepts of covering type theory and its applications in algebraic topology through expert insights and mathematical frameworks.

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

Learning from Two-Parameter Persistent Homology Using Graphcodes

Discover graphcodes, a novel representation for two-parameter persistent homology that provides efficient computation and interpretable summaries for machine learning applications.

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

Steady and Ranging - Persistence Without Homology

Explore steady and ranging persistence functions as extensions of persistent homology, covering stability results and applications to graphs, digraphs, and hypergraphs.

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

A Chordless Cycle Filtration for Network Dimensionality Detection

Discover a novel topological data analysis approach using chordless cycles to estimate the dimensionality of complex networks with hyperbolic geometry through neural network methods.

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

Estimating the Persistent Homology of R^n-Valued Functions Using Functional-Geometric Multifiltrations

Discover how to approximate persistent homology of multidimensional functions from finite samples using functional-geometric multifiltrations with statistical convergence guarantees.

• YouTube
• 1 hour 6 minutes
• Self-Paced
• Free Video

LS-Category and Topological Complexity of Real Torus Manifolds and Dold Manifolds

Explore LS-category and topological complexity computations for real torus manifolds and Dold manifolds, including sharp bounds and applications to generalized real Bott manifolds.

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

The Persistence of Painting Styles

Discover how persistent homology objectively analyzes artistic styles, differentiating between artists and detecting AI-generated art with statistical certainty.

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