Applied Algebraic Topology Network Courses

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

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

Stabilizing Decomposition of Multiparameter Modules

Explores stability theories for multiparameter module decomposition, addressing challenges and presenting recent findings. Discusses potential strengthening of stability results for staircase decomposable modules.

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

Urysohn Width

Explore the 100-year history and applications of Urysohn width, a metric invariant quantifying space approximation by simplicial complexes. Discover its role in dimension theory and modern geometric challenges.

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

An Upper Bound on the Sequential Topological Complexity

Exploring upper bounds on sequential topological complexity in robot motion planning, with applications to lens spaces and improved dimensional upper bounds under group actions.

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

Vietoris-Rips Complexes of Hypercube Graphs

Explore Vietoris-Rips complexes of hypercube graphs, their collapsibility, and applications in genetic trees and persistent homology. Gain insights into simplicial complexes and topological data analysis.

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

Dejan Govc - Fundamental Groups of Small Simplicial Complexes

Explore minimal triangulations of manifolds and fundamental groups of small simplicial complexes, with insights on estimating vertex counts in minimal triangulations.

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

Efficient Invariant Embeddings for Universal Equivariant Learning

Explore efficient invariant embeddings for universal equivariant learning, focusing on group symmetries in machine learning tasks and their applications in various architectures like CNNs and graph neural networks.

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

Optimal Topological Simplification of Surfaces

Algorithmes et résultats de complexité pour simplifier la topologie des surfaces de manière optimale, en utilisant des courbes et graphes les plus courts possible.

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

Persistence Diagram Bundles- A Multidimensional Generalization of Vineyards

Explore persistence diagram bundles, a multidimensional generalization of vineyards for analyzing topological changes in data sets with multiple parameters, including computation methods and potential applications.

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

Analyzing Point Processes Using Topological Data Analysis

Explore point processes using topological data analysis, covering models, statistical techniques, and applications in spatial statistics. Learn to distinguish between process types and understand central limit theorems.

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

MD Simulations and Machine Learning to Quantify Interfacial Hydrophobicity

Explore molecular dynamics simulations and machine learning techniques to analyze interfacial hydrophobicity, focusing on efficient data analysis methods and topological approaches for complex chemical systems.

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

Yusu Wang - Graph Neural Network: Representational Power and Limitations

Explore graph neural networks' power and limitations, focusing on representation capabilities, Weisfeiler-Lehman tests, and universal approximation results for informed practical applications.

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

The Role of Solvent in Crystal Nucleation from Solution

Explore crystal nucleation mechanisms and solvent effects using advanced simulation methods. Gain insights into polymorph selection and solvent-dependent nucleation processes for various substances.

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