Applied Algebraic Topology Network Courses

On the Rational Topological Complexity of Coformal Elliptic Spaces

Explore rational topological complexity bounds for elliptic spaces, focusing on coformal cases where it aligns with rational homotopy dimension.

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

Recent Advances in Theory and Implementation of Multi-Parameter Persistence

Explores recent developments in multi-parameter persistence, covering stable filtrations and discrete descriptors. Includes interactive clustering software demo and discusses extensions of one-parameter persistence concepts.

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

The Lower Semi-Continuity of Pi_1 and Nilpotent Structures in Persistence

Explore lower semi-continuity of π₁ in non-compact spaces, examining symmetries and nilpotent structures in persistence theory for compact geodesic space sequences.

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

Configuration Spaces of Hard Squares

Exploring topology of configuration spaces with hard squares, focusing on Betti numbers' growth rate in confined regions. New insights into complex geometric arrangements.

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

Topological Optimization with Big Steps

Explore persistent homology for optimization, using cycles and chains to prescribe gradients. Learn about a linear-time algorithm for special cases and its practical benefits in reducing optimization steps.

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

Symmetric and Symmetrized Topological Complexity of the Torus

Explore symmetric and symmetrized topological complexity of the torus, completing the description for closed surfaces using obstruction theory and explicit resolution of integers over full braid group.

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

Effective Computation of Spectral Systems and Relation With Multi-Parameter Persistence

Explore algorithms for computing spectral systems in Computational Algebraic Topology, their implementation in Kenzo, and applications to multi-parameter persistence, including spaces of infinite type.

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

Minimal Cycle Representatives in Persistent Homology Using Linear Programming

Explores optimization techniques for selecting minimal cycle representatives in persistent homology, comparing effectiveness and computational costs of various algorithms using linear programming methods.

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

Torsion Homology Growth and Related Topics

Explore torsion homology growth in compact CW complexes, examining Betti number growth in finite covers and connections to amenable category and minimal volume entropy.

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

Shape of Data in Biology - Extending the PH Pipeline

Exploring spatial structure in biological data using topological data analysis, with focus on knotted proteins and introducing hyperTDA for interpretable, automated analysis of complex systems.

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

Non-Diffusive Vortexes at Transition State of Activated Process by Persistent Homology

Exploring non-diffusive dynamics in molecular transitions using persistent homology, revealing reactive vortexes and rotational fluxes at transition states of alanine-dipeptide isomerization.

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

Kohei Tanaka - Sectional Category for Maps of Finite Spaces

Explore combinatorial approaches to sectional category in finite T_0 spaces, examining McCord maps, weak homotopy equivalences, and Fadell-Neuwirth fibrations through computational examples.

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

Alpha Magnitude

Explores alpha magnitude, a new metric space invariant, its properties, and potential for estimating fractal dimensions in real-world datasets, offering computational advantages over existing methods.

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

A Hierarchical Approach to Crystal Structure Prediction

Explore a hierarchical approach to crystal structure prediction for organic molecules, focusing on methodology requirements, algorithms, and applications in pharmaceutical and agrochemical industries.

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

The Directional Transform

Explore the directional transform in topological data analysis, its applications in understanding complex structures, and its potential for enhancing machine learning models and data shape quantification.

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