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#Homotopy

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Simons Semester on Dynamics

When Topology Forces Dynamics - Lecture 1

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Explore topological dynamics, focusing on how topology influences system behavior. Gain insights into fixed point index, Nielsen theory, and homotopy stability theorems.
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29 Lesons
1 hour 35 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Grupo Fundamental e Espaços de Recobrimento - Aula 18

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Explore conceitos avançados de topologia algébrica, incluindo homotopia, grupo fundamental e espaços de recobrimento. Aprofunde-se em teoremas importantes e aplicações em superfícies compactas.
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1 Lesons
2 hours 16 minutes
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Instituto de Matemática Pura e Aplicada

Grupo Fundamental e Espaços de Recobrimento - Aula 09

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Explore conceitos avançados de topologia algébrica, incluindo homotopia, grupo fundamental e espaços de recobrimento. Aprofunde-se em teoremas importantes e aplicações em superfícies compactas.
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1 Lesons
1 hour 35 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Grupo Fundamental e Espaços de Recobrimento - Aula 08

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Explore conceitos avançados de topologia algébrica, incluindo homotopia, grupo fundamental e espaços de recobrimento. Aprofunde-se em teoremas importantes e aplicações em superfícies compactas e espaços projetivos.
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1 Lesons
1 hour 56 minutes
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Instituto de Matemática Pura e Aplicada

Grupo Fundamental e Espaços de Recobrimento - Aula 07

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Explore conceitos avançados de topologia algébrica, incluindo homotopia, grupo fundamental, espaços de recobrimento e suas aplicações em geometria e análise matemática.
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1 Lesons
2 hours 1 minute
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Free-Video
Instituto de Matemática Pura e Aplicada

Grupo Fundamental e Espaços de Recobrimento - Aula 06

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Explore conceitos avançados de topologia algébrica, incluindo homotopia, grupo fundamental e espaços de recobrimento. Aprofunde-se em teoremas importantes e aplicações em superfícies compactas e espaços projetivos.
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1 Lesons
2 hours 24 minutes
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Instituto de Matemática Pura e Aplicada

Grupo Fundamental e Espaços de Recobrimento - Aula 22

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Explore conceitos avançados de topologia algébrica, incluindo homotopia, grupo fundamental e espaços de recobrimento. Aprofunde-se em teoremas importantes e aplicações em superfícies compactas e espaços projetivos.
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1 Lesons
2 hours 38 minutes
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Instituto de Matemática Pura e Aplicada

Grupo Fundamental e Espaços de Recobrimento - Aula 21

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Explore conceitos avançados de topologia algébrica, incluindo homotopia, grupo fundamental, espaços de recobrimento e suas aplicações em geometria e topologia.
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1 Lesons
2 hours 12 minutes
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Instituto de Matemática Pura e Aplicada

Grupo Fundamental e Espaços de Recobrimento - Aula 20

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Explore conceitos avançados de topologia algébrica, incluindo homotopia, grupo fundamental, espaços de recobrimento e suas aplicações em geometria e análise matemática.
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1 Lesons
2 hours 5 minutes
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Free-Video
Instituto de Matemática Pura e Aplicada

Grupo Fundamental e Espaços de Recobrimento - Aula 19

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Explore conceitos avançados de topologia algébrica, incluindo homotopia, grupo fundamental, espaços de recobrimento e suas aplicações em geometria e análise matemática.
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1 Lesons
2 hours 11 minutes
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Instituto de Matemática Pura e Aplicada

Grupo Fundamental e Espaços de Recobrimento - Aula 12

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Explore conceitos avançados de topologia algébrica, incluindo homotopia, grupo fundamental e espaços de recobrimento. Aprofunde-se em teoremas importantes e aplicações em superfícies compactas e espaços projetivos.
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1 Lesons
1 hour 35 minutes
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Free-Video
Instituto de Matemática Pura e Aplicada

Grupo Fundamental e Espaços de Recobrimento - Aula 11

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Explore conceitos avançados de topologia algébrica, incluindo homotopia, grupo fundamental, espaços de recobrimento e suas aplicações em geometria e análise matemática.
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1 Lesons
2 hours 4 minutes
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Instituto de Matemática Pura e Aplicada

Grupo Fundamental e Espaços de Recobrimento - Aula 10

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Explore conceitos avançados de topologia algébrica, incluindo homotopia, grupo fundamental e espaços de recobrimento. Aprofunde-se em teoremas importantes e aplicações em superfícies compactas e espaços projetivos.
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1 Lesons
1 hour 59 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Grupo Fundamental e Espaços de Recobrimento - Aula 17

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Explore conceitos avançados de topologia algébrica, incluindo homotopia, grupo fundamental, espaços de recobrimento e suas aplicações em geometria e análise matemática.
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1 Lesons
2 hours 7 minutes
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Free-Video
Instituto de Matemática Pura e Aplicada

Grupo Fundamental e Espaços de Recobrimento - Aula 16

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Explore conceitos avançados de topologia algébrica, incluindo homotopia, grupo fundamental e espaços de recobrimento. Aprofunde-se em teoremas importantes e aplicações em superfícies compactas e espaços projetivos.
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1 Lesons
2 hours 5 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Grupo Fundamental e Espaços de Recobrimento - Aula 15

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Explore conceitos avançados de topologia algébrica, incluindo homotopia, grupo fundamental, espaços de recobrimento e suas aplicações em geometria e análise matemática.
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1 Lesons
2 hours 4 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Grupo Fundamental e Espaços de Recobrimento - Aula 14

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Explore conceitos avançados de topologia algébrica, incluindo homotopia, grupo fundamental, espaços de recobrimento e suas aplicações em geometria e topologia.
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1 Lesons
2 hours 11 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Grupo Fundamental e Espaços de Recobrimento - Aula 13

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Explore conceitos avançados de topologia algébrica, incluindo homotopia, grupo fundamental e espaços de recobrimento. Aprofunde-se em teoremas importantes e aplicações em superfícies compactas e espaços projetivos.
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1 Lesons
2 hours 13 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Grupo Fundamental e Espaços de Recobrimento - Aula 03

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Explore conceitos avançados de topologia algébrica, incluindo homotopia, grupo fundamental e espaços de recobrimento. Aprofunde-se em aplicações e teoremas fundamentais da área.
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1 Lesons
2 hours 3 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Mestrado: Grupo Fundamental e Espaços de Recobrimento - Aula 01

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Explore conceitos fundamentais de topologia algébrica, incluindo homotopia, grupo fundamental e espaços de recobrimento. Aprenda aplicações práticas e teoremas importantes nesta aula introdutória de mestrado.
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15 Lesons
1 hour 56 minutes
On-Demand
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Applied Algebraic Topology Network

Geometric Interpretation of Persistence

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Explore geometric interpretations of persistence in algebraic topology, covering space reconstruction, one-dimensional persistent homology classification, and detection of contractible geodesics using higher-dimensional features.
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20 Lesons
1 hour 1 minute
On-Demand
Free-Video
Applied Algebraic Topology Network

Henry Adams - Vietoris-Rips Complexes of Hypercube Graphs

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Explore Vietoris-Rips complexes of hypercube graphs, their homotopy types, and applications in genetic recombination and persistent homology. Discover formulas, open questions, and conjectures in this fascinating area of applied algebraic topology.
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13 Lesons
45 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

The Vietoris Rips Complex of the Circle

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Explore the Vietoris-Rips complex of the circle, its homotopy types at different thresholds, and implications for persistent homology in topological data analysis.
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1 Lesons
57 minutes
On-Demand
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Applied Algebraic Topology Network

Vietoris-Rips Persistent Homology, Injective Metric Spaces, and The Filling Radius

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Explore geometric persistent homology, its isomorphism with Vietoris-Rips filtration, and applications in characterizing persistence barcodes, bounding intervals, and connecting to filling radius.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
IMSA

Braids and Configuration Spaces

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Explore topology, homotopy, and braid groups in this talk on configuration spaces. Discover connections between fundamental groups, loop spaces, and unordered configurations in mathematics.
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19 Lesons
56 minutes
On-Demand
Free-Video
QuantumTopology

Picture Valued Invariants, Groups, and Applications of Virtual Knot Theory

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Explore picture valued invariants, groups, and applications of virtual knot theory with Professor Vassily Manturov in this advanced mathematics lecture.
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11 Lesons
55 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Mikhail Katz - Collapsing Surfaces

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Exploring surface collapse in Riemannian geometry, focusing on critical points, intersection theory, and Toponogov comparison. Analyzes fiber homotopy and discrete integration against Euler characteristic.
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10 Lesons
50 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Data Complexes, Obstructions, Persistent Data Merging

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Explore data complexes, topological obstructions in database JOIN operations, and persistence levels in data alignment. Learn about measure theory, homotopy, and homology in the context of data integration.
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24 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

Computing Optimal Homotopies

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Explore optimal curve similarity measures using homotopy-based approaches, examining structural properties, algorithms, and open questions in topology and computational geometry.
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20 Lesons
47 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Computing Optimal Homotopies

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Explore curve similarity measures and homotopy-based deformations in GIS, medical imaging, and graphics. Survey geometric and topological metrics, algorithms, and open questions in optimal homotopy computation.
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1 Lesons
59 minutes
On-Demand
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Applied Algebraic Topology Network

Two Methods of Efficiently Approximating Semi-Algebraic Sets Up to Homotopy

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Explores efficient methods for approximating semi-algebraic sets, focusing on singly exponential complexity algorithms and their applications in algebraic geometry.
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1 Lesons
1 hour
On-Demand
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Applied Algebraic Topology Network

Antonio Rieser - Algebraic Topology for Graphs and Mesoscopic Spaces

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Explore algebraic topology for graphs and mesoscopic spaces, covering homotopy, homology, and metric cohomology. Learn about pseudotopological spaces and their applications in various mathematical categories.
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1 Lesons
54 minutes
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International Mathematical Union

Homotopy Patterns in Group Theory

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Explore homotopy patterns in group theory, delving into advanced mathematical concepts and their applications in topology and algebra.
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1 Lesons
43 minutes
On-Demand
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ICTP Mathematics

Topology - Lecture 10

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Explore advanced concepts in topology, including complex geometric structures and their properties, in this comprehensive lecture by mathematician Bruno Zimmerman.
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1 Lesons
1 hour 29 minutes
On-Demand
Free-Video
ICTP Mathematics

Topology - Lecture 4

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Explore fundamental concepts of topology, including continuous functions, homeomorphisms, and topological properties, in this advanced mathematics lecture.
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1 Lesons
1 hour 40 minutes
On-Demand
Free-Video
ICTP Mathematics

Topology - Lecture 6

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Explore fundamental concepts and advanced techniques in topological spaces, including continuity, compactness, and connectedness, with expert guidance from Bruno Zimmerman.
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1 Lesons
1 hour 37 minutes
On-Demand
Free-Video
ICTP Mathematics

Topology - Lecture 2

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Explore fundamental concepts of topology, including topological spaces, continuity, and homeomorphisms, with a focus on mathematical rigor and abstract reasoning.
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1 Lesons
1 hour 35 minutes
On-Demand
Free-Video
ICTP Mathematics

Topology - Lecture 3

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Explore fundamental concepts of topology, including continuous functions, homeomorphisms, and topological properties, in this advanced mathematics lecture.
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1 Lesons
1 hour 37 minutes
On-Demand
Free-Video
ICTP Mathematics

Topology - Lecture 14

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Explore advanced concepts in topology with Bruno Zimmerman, delving into complex mathematical structures and their properties in this comprehensive lecture.
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1 Lesons
1 hour 34 minutes
On-Demand
Free-Video
ICTP Mathematics

Topology - Lecture 8

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Explore fundamental concepts and advanced techniques in topological spaces, manifolds, and algebraic topology with expert guidance from Bruno Zimmerman.
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1 Lesons
1 hour 36 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Topological and Combinatorial Models of Directed Path Spaces

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Explore topological and combinatorial models for directed path spaces in concurrency theory, focusing on methods to analyze execution paths and state spaces in computer science.
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1 Lesons
1 hour 25 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

A Sheaf-Theoretic Construction of Shape Space

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Sheaf-theoretic approach to construct shape space using Persistent Homology Transform. Explores homotopy sheaves, metrics, stability theorems, and approximation of manifolds.
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1 Lesons
53 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Skeletonization Algorithms With Theoretical Guarantees for Point Clouds

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Explore skeletonization algorithms for point clouds, including Mapper, alpha-Reeb graphs, and Homologically Persistent Skeleton. Compare their performance on synthetic and real data sets.
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1 Lesons
1 hour 1 minute
On-Demand
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ACM SIGPLAN

Taylor Expansion and Game Semantics - Exploring Isomorphisms in Lambda Calculus

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Explore the isomorphism between Taylor expansion of λ-terms and pointer concurrent games interpretation, extending previous results on resource terms and game semantics.
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1 Lesons
18 minutes
On-Demand
Free-Video