Topological Complexity Courses and Certifications

Applied Algebraic Topology Network

Topological Complexity Seminar - Applied Algebraic Topology Network

Explore advanced mathematical concepts in topological complexity through expert seminars covering motion planning, manifold theory, and algebraic topology applications.

• YouTube
• 1 day 17 hours 29 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Effectual Topological Complexity

Explora la Complejidad Topológica Efectual, una nueva versión para G-Espacios. Aprende sus propiedades, relación con TC estándar y aplicación en superficies, especialmente en el toro.

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

Applied Algebraic Topology Network

Topological Complexity Using Arbitrary Covers

Explore topological complexity using arbitrary covers, focusing on sectional category, ANRs, and generalized concepts. Gain insights into advanced algebraic topology techniques and applications.

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

Applied Algebraic Topology Network

Topological Complexity of Pure Graph Braid Groups

Explore topological complexity in graph braid groups, focusing on Farber's conjecture about ordered configuration spaces and its implications for topological robotics.

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

Applied Algebraic Topology Network

An Upper Bound on the Topological Complexity of Discriminantal Varieties

Explore upper bounds on topological complexity of discriminantal varieties, with applications to configuration spaces. Combines Morse theory, equivariant homotopy theory, and complex geometry.

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

Applied Algebraic Topology Network

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
• On-Demand
• Free Video

Applied Algebraic Topology Network

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

Applied Algebraic Topology Network

Michael Farber - Topological Complexity of Spherical Bundles

Explore parametrized motion planning algorithms and the topological complexity of sphere bundles, examining characteristic classes and specific examples in applied algebraic topology.

• YouTube
• 1 hour 14 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Topological Complexity for Manifolds with Abelian Fundamental Group

Explores conditions for nonmaximal topological complexity in manifolds with abelian fundamental groups, generalizing results on spaces with small fundamental groups and nonorientable surfaces.

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

Applied Algebraic Topology Network

Bedlewo- Topological Complexity and the Motion Planning Problem in Robotics

Explore topological complexity in robotics motion planning, its algebraic topology properties, recent developments, and research trends in this rich field.

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

Applied Algebraic Topology Network

Steve Scheirer - Relative Topological Complexity and Configuration Spaces

Explore relative topological complexity and configuration spaces in this advanced algebraic topology talk, covering definitions, results, and applications.

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

Applied Algebraic Topology Network

Bounds for the Higher Topological Complexity of Configuration Spaces

Explore bounds for higher topological complexities in unordered configuration spaces of trees and anchored configuration spaces of circles with two anchor points.

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

Applied Algebraic Topology Network

Musing About Robotic Football

Explore robotic football strategies, discussing modeling, non-fibrations, speed, sensing, and topological complexity in the context of navigating blockers to score.

• YouTube
• 1 hour 4 minutes
• On-Demand
• Free Video

Applied Algebraic Topology Network

Wanted- Topologists for Autonomous Robots Community

Exploring topological complexity in robotics: from path planning to task spaces. Insights into rigorous formulations for robotic autonomy, emphasizing environment topology and combinatorics in cooperative motion.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

Fields Institute

Surfaces in 3-Manifolds and the Thurston Norm

Explore the Thurston norm in 3-manifold topology, its significance in measuring surface complexity, and its role in understanding modern topological breakthroughs.

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