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#Topological Complexity

Showing: 30 courses
Santa Fe Institute

Autodiagnosis and the Dynamical Emergence Theory of Basic Consciousness

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Explore the theory of basic consciousness, its emergence, and related concepts like energy landscapes and metastable states in this thought-provoking discussion on the nature of experience.
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18 Lesons
1 hour 13 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Effectual Topological Complexity

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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.
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6 Lesons
29 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Topological Complexity Using Arbitrary Covers

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Explore topological complexity using arbitrary covers, focusing on sectional category, ANRs, and generalized concepts. Gain insights into advanced algebraic topology techniques and applications.
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13 Lesons
55 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Musing About Robotic Football

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Explore robotic football strategies, discussing modeling, non-fibrations, speed, sensing, and topological complexity in the context of navigating blockers to score.
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14 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Topological Complexity of Pure Graph Braid Groups

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Explore topological complexity in graph braid groups, focusing on Farber's conjecture about ordered configuration spaces and its implications for topological robotics.
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10 Lesons
56 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

An Upper Bound on the Topological Complexity of Discriminantal Varieties

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Explore upper bounds on topological complexity of discriminantal varieties, with applications to configuration spaces. Combines Morse theory, equivariant homotopy theory, and complex geometry.
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10 Lesons
54 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Bedlewo- Topological Complexity and the Motion Planning Problem in Robotics

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Explore topological complexity in robotics motion planning, its algebraic topology properties, recent developments, and research trends in this rich field.
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16 Lesons
1 hour 33 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Enrique Torres-Giese - Sequential Motion Planning Assisted by Group Actions

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Sequential motion planning with group actions: exploring effectual and effective TC, orbital topological complexity, and their relationships. Calculations for actions on orientable surfaces and spheres included.
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9 Lesons
38 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Steve Scheirer - Relative Topological Complexity and Configuration Spaces

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Explore relative topological complexity and configuration spaces in this advanced algebraic topology talk, covering definitions, results, and applications.
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13 Lesons
50 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Jamie Scott - Applications of Surgery to a Generalized Rudyak Conjecture

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Exploring applications of surgery theory to Rudyak's conjecture, discussing generalizations to topological complexity, and examining cases for simply connected codomains.
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12 Lesons
50 minutes
On-Demand
Free-Video
Fields Institute

Surfaces in 3-Manifolds and the Thurston Norm

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Explore the Thurston norm in 3-manifold topology, its significance in measuring surface complexity, and its role in understanding modern topological breakthroughs.
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8 Lesons
57 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Topological Complexity of Fibrations and Covering Maps

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Explore topological complexity of fibrations and covering maps, examining their homotopy invariance and applications in robotics and mechanical device manipulation.
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1 Lesons
47 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Bedlewo - Topological Complexity of the Klein Bottle

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Explore the topological complexity of non-orientable surfaces, focusing on the Klein bottle and extending findings to surfaces of genus ≥2. Collaborative research insights shared.
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1 Lesons
39 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Wanted- Topologists for Autonomous Robots Community

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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.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Symmetric and Symmetrized Topological Complexity of the Torus

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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.
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1 Lesons
33 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Homotopic Distance and Generalized Motion Planning

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Explore homotopic distance between maps, unifying Lusternik-Schnirelmann category and topological complexity. Learn how Morse-Bott functions and navigation functions apply to generalized motion planning problems.
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1 Lesons
41 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Topological Complexity for Manifolds with Abelian Fundamental Group

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Explores conditions for nonmaximal topological complexity in manifolds with abelian fundamental groups, generalizing results on spaces with small fundamental groups and nonorientable surfaces.
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1 Lesons
57 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Bredon Cohomology and LS-Categorical Invariants

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Explore Bredon cohomology's role in estimating topological complexity of aspherical spaces and its application to equivariant LS-category of groups with operators.
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1 Lesons
58 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

The Topological Complexity of Pure Graph Braid Groups Is Stably Maximal

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Explore the topological complexity of configuration spaces in graphs, using group theoretic estimates for higher topological complexity instead of traditional cohomology approaches.
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1 Lesons
49 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Michael Farber - Topological Complexity of Spherical Bundles

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Explore parametrized motion planning algorithms and the topological complexity of sphere bundles, examining characteristic classes and specific examples in applied algebraic topology.
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1 Lesons
1 hour 14 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Higher Topological Complexity of Seifert Fibered Manifolds

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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.
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1 Lesons
49 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

An Upper Bound on the Sequential Topological Complexity

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Exploring upper bounds on sequential topological complexity in robot motion planning, with applications to lens spaces and improved dimensional upper bounds under group actions.
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1 Lesons
47 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Bounds for the Higher Topological Complexity of Configuration Spaces

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Explore bounds for higher topological complexities in unordered configuration spaces of trees and anchored configuration spaces of circles with two anchor points.
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1 Lesons
58 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Effective Topological Complexity and Effective Lusternik-Schnirelmann Category

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Exploring effective topological complexity and Lusternik-Schnirelmann category in motion planning, focusing on symmetries in configuration spaces and their impact on problem complexity.
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1 Lesons
1 hour 10 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Sequential Parametrized Topological Complexity of Sphere Bundles

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Introduction to sequential parametrized motion planning and its application to sphere bundles, exploring algorithms that navigate systems through prescribed states while adapting to variable external conditions.
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1 Lesons
57 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Topological Complexity of Monotone Symplectic Manifolds

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Explore topological complexity in 4D spherically monotone manifolds, focusing on Kodaira dimension estimation and its implications for symplectic geometry.
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1 Lesons
55 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Disk Configuration Spaces and Topological Complexity

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Exploring disk configuration spaces, their topology, and topological complexity, focusing on ordered configurations of unit-diameter disks in infinite strips and their geometric implications.
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1 Lesons
51 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Right-Angled Artin Subgroups of Graph Braid Groups

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Explore right-angled Artin subgroups in graph braid groups, examining recent conjectures and their applications to topological complexity in algebraic topology.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Distributional and Intertwining Invariants of Manifolds

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Delve into advanced algebraic topology concepts, exploring distributional LS-category, sequential topological complexity, and intertwining invariants in manifolds, with applications to motion planning.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Sequential Topological Complexity of Group Homomorphisms

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Delve into advanced algebraic topology concepts, exploring sequential topological complexity of maps and group homomorphisms through detailed mathematical analysis and computations.
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1 Lesons
49 minutes
On-Demand
Free-Video