Applied Algebraic Topology Network Courses

The Intrinsic Volumes of a Space Filling Diagram and Their Derivatives

Explore intrinsic volumes in molecular dynamics, focusing on space-filling diagrams and their derivatives. Learn formulas for weighted volumes and curvatures in Alpha shape representations.

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

On the Role of Group Equivariant Non-Expansive Operators in TDA

Explore group equivariant non-expansive operators as tools for approximating data observers in Topological Data Analysis, focusing on their mathematical properties and applications.

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

Kathryn Hess Interviewed by Peter Bubenik - August 11, 2021

Engaging interview with mathematician Kathryn Hess, exploring her research, insights, and contributions to applied algebraic topology and related fields.

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

Parallel Decomposition of Persistence Modules Through Interval Bases

Explore parallel decomposition of persistence modules using interval bases, enhancing Topological Data Analysis with distributed computation and Hodge decomposition techniques.

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

Cell Complex Neural Networks

Exploring neural network computations on cell complexes, generalizing graph neural networks and introducing inter-cellular message passing schemes that consider underlying topology.

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

Topological Data Analysis Based Machine Learning Models for Drug Design

Explores TDA-based models for effective molecular representation in drug design, combining persistent homology, spectral models, and Ricci curvature with machine learning for improved performance.

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

Universes as Bigdata- From Geometry, to Physics, to Machine-Learning

Explore the intersection of string theory, geometry, and machine learning in physics, examining how AI aids mathematical research across various fields.

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

Rips Complexes, Projective Codes, and Zeros of Odd Maps

Explore connections between Rips complexes, projective codes, and odd map zeros, bridging discrete geometry and topology. New insights into sphere Rips complexes' challenging nature.

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

Homotopic Distance and Generalized Motion Planning

Explore homotopic distance between maps, unifying Lusternik-Schnirelmann category and topological complexity. Learn how Morse-Bott functions and navigation functions apply to generalized motion planning problems.

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

Multiscale Many-body Correlations and Structure in Chemistry Data

Integrating graphs, topology, and geometry to analyze complex chemistry data, providing insights into multiscale correlations and structures beyond traditional methods.

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

Vietoris-Rips Complexes and Geometric Group Theory

Explore Vietoris-Rips complexes in geometric group theory, focusing on topological finiteness properties, hyperbolic groups, and recent developments in Morse theory and persistent homology.

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

Homology of Graphs and Hypergraphs

Explore topological structures of graphs and hypergraphs, including recent findings on homology and persistent homology, with applications in combinatorial and metric space analysis.

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

Bridging Applied and Quantitative Topology

Survey of emerging connections between applied and quantitative topology, focusing on Vietoris-Rips complexes and their applications in computational topology, geometric group theory, and dataset shape approximation.

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

Practical Clustering and Topological Data Analysis

Explore clustering algorithms and topological data analysis from a data science perspective, covering techniques from k-means to DBSCAN and dimensionality reduction methods like UMAP.

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

Homotopy Types of Vietoris–Rips Complexes of Metric Gluings

Explore homotopy types of Vietoris-Rips complexes in metric wedge sums and gluings, with applications to persistent homology of metric graphs and insights into open research directions.

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