Applied Algebraic Topology Network Courses

Quantum Topological Data Analysis - Part 1

1 review

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
• On-Demand
• Free Video

Kelin Xia - Persistent Function Based Machine Learning for Drug Design

1 review

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
• On-Demand
• Free Video

Higher Topological Complexity of Seifert Fibered Manifolds

Explore LS-category and topological complexity of Seifert fibered manifolds, examining lower bounds for higher TC using cohomology class weights and deriving TC_n ranges.

• YouTube
• 49 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

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

The Asymptotics of Betti Numbers in Preferential Attachment Clique Complexes

Explore the higher-order connectivity of preferential attachment networks through Betti numbers, examining growth rates and asymptotic behavior in this advanced mathematical analysis.

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

A Sheaf-based Approach to Graph Neural Networks

Explore sheaf theory's application to Graph Neural Networks, offering a novel perspective on Geometric Deep Learning beyond traditional geometric structures.

• YouTube
• 1 hour 1 minute
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• Free Video

Dimensionality Reduction via Distributed Persistence - DIPOLE

Explore dimensionality reduction with DIPOLE, a novel approach combining local metric and global topological preservation for improved data visualization and analysis.

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