Applied Algebraic Topology Network Courses

Quantum Topological Data Analysis - Part 1

1 rating

Explore quantum persistent homology algorithms for pattern recognition in data, leveraging quantum computing's potential to enhance traditional Topological Data Analysis methods and improve efficiency.

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

Kelin Xia - Persistent Function Based Machine Learning for Drug Design

1 rating

Exploring persistent function-based machine learning for drug design, focusing on novel molecular representations and their application in improving predictive models for drug discovery.

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

Constrained Motion Spaces in Robotic Arms

Explore topological approaches to robotic motion planning by computing homology groups of constrained robotic arm motion spaces using Morse theory and combinatorial methods.

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

DONUT - Database of Original Non-theoretical Uses of Topology

Discover how to navigate and contribute to DONUT, a specialized database cataloging practical applications of topology across various fields and research domains.

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

Stability of Rips-Type Ellipsoid Complexes

Explore Rips-type ellipsoid complexes using local PCA to better capture manifold geometry, with theoretical stability guarantees for persistence barcodes under data variations.

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

Robustness of Persistent Topological Features and Minimum Homological Cuts

Explore adversarial robustness in persistent homology, connecting topological data analysis to minimum cut problems in simplicial complexes for outlier-resistant feature detection.

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

A New Kind of Cell-Complex for Poset Topology

Explore CL-complexes, a novel cell-complex framework for representing finite poset homotopy types, extending beyond traditional order complexes with applications to higher-order nerve theorems.

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

SuPerPoV - Score and Evolution of the Stratospheric Polar Vortex via Persistent Homology

Discover a threshold-free method using persistent homology to classify the stratospheric polar vortex into displaced, split, or normal states.

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

Coupling Time-Aware Multipersistence with Graph CNNs for Time Series Forecasting

Explore innovative time series forecasting using Graph Neural Networks and multipersistence, applied to traffic flow, cryptocurrency prices, and COVID-19 hospitalizations.

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

Parallel Decomposition of Persistence Modules Through Interval Bases

Exploring parallel decomposition of persistence modules using interval bases, with applications in Topological Data Analysis and connections to the Hodge Laplacian.

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

Simplicial Neural Networks

Explore simplicial neural networks, a generalization of graph neural networks for multi-dimensional data, and their applications in imputing missing data on coauthorship complexes.

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

How Math and AI Are Revolutionizing Biosciences

Exploring how mathematics and AI revolutionize biosciences, focusing on tackling challenges in biological data complexity, dimensionality, and nonlinearity to enhance AI's capabilities in drug design and viral mutation prediction.

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

Solving Systems of ODEs via Combinatorial Homological Algebra

Exploring efficient computation of homological representations in dynamical systems, with applications to differential equations and parameter space analysis.

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

Vidit Nanda - Principal Components Along Quiver Representations

Principal components analysis for quiver representations: dimensionality reduction, comparison, and optimization techniques for vector-space valued representations across pure and applied mathematics.

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

The Topological Dirac Operator and the Dynamics of Topological Signals

Explore topological signals, higher-order Laplacians, and the Dirac operator in network science. Learn about spectral properties, diffusion dynamics, and topological synchronization in simplicial complexes and multiplex networks.

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