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IMSA

The $K(\pi, 1)$ Conjecture - Part 2

1 rewiews
Explore the recent proof of the classical K(π,1) conjecture for affine Artin groups, delving into its mathematical intricacies and implications for algebraic topology.
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1 Lesons
56 minutes
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Free-Video
Applied Algebraic Topology Network

Quantum Topological Data Analysis - Part 1

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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.
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1 Lesons
26 minutes
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Free-Video
M-Seminar, Kansas State University

Cohomological Hall Algebra of Cyclic Quivers and Integral Form of Affine Yangians

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Explore the intricate world of Hall algebra-type constructions and their applications in a lecture by Shivang Jindal from the University of Edinburgh. Delve into the complexities of studying algebras related to the moduli space of representations of the…
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1 Lesons
1 hour 17 minutes
On-Demand
Free-Video
Prague Mathematical Physics Seminar

Linear BV Quantization as a Functor of Infinity Categories - Lecture

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Dive into linear BV quantization as a functor of infinity categories, exploring advanced mathematical concepts in this Prague Mathematical Physics Seminar.
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1 Lesons
1 hour 39 minutes
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Free-Video
University of Chicago Department of Mathematics

The Fundamental Group of Random 3-Manifolds and Other Random Objects

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Dive into the fundamental group of random 3-manifolds, exploring probability distributions and their applications to various categories in mathematics.
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1 Lesons
1 hour 6 minutes
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Free-Video
University of Chicago Department of Mathematics

Cohomology of Moduli Spaces of Curves

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Dive into the cohomology of moduli spaces of curves with Hannah Larson. Explore tautological rings, compactifications, and the mysteries of non-tautological cohomology groups in algebraic geometry.
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1 Lesons
1 hour 3 minutes
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Free-Video
University of Chicago Department of Mathematics

The Weil Conjectures and A1-homotopy Theory

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Dive into the Weil Conjectures and A1-homotopy theory, exploring connections between algebraic topology and finite field equations in this mathematical colloquium.
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1 Lesons
1 hour 7 minutes
On-Demand
Free-Video
University of Chicago Department of Mathematics

Courant, Bezout, and Persistence - Lecture 2

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Explore spectral geometry through persistence modules and barcodes, examining oscillation of functions and applications to Courant's nodal domain theorem and Bezout's theorem in eigenfunctions.
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1 Lesons
1 hour 9 minutes
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University of Chicago Department of Mathematics

Courant, Bezout, and Persistence in Spectral Geometry - Lecture 1

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Explore spectral geometry and topological persistence, focusing on oscillation of functions, Courant's nodal domain theorem, and Bezout's theorem in the context of eigenfunctions.
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1 Lesons
58 minutes
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Free-Video
Simons Semester on Dynamics

Methods for Studying Abelian Actions and Centralizers - Lecture 3

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Explore two methods for studying abelian actions and centralizers: linearization and non-linearization. Delve into cohomology concepts and their applications in dynamical systems analysis.
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1 Lesons
1 hour 3 minutes
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Dr Trefor Bazett

Intro to the Fundamental Group - Algebraic Topology with Tom Rocks Maths

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Explore algebraic topology and the fundamental group, from basic concepts to advanced applications like Brouwer's Fixed Point Theorem. Learn to analyze spaces through continuous deformations and group theory.
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10 Lesons
44 minutes
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Institute for Advanced Study

A Gentle Approach to Crystalline Cohomology - Jacob Lurie

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Explore crystalline cohomology and the de Rham-Witt complex in algebraic geometry, with insights on alternative constructions and applications in positive characteristic fields.
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15 Lesons
56 minutes
On-Demand
Free-Video
Institute for Advanced Study

Lie Algebras and Homotopy Theory - Jacob Lurie

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Explore connections between Lie algebras and homotopy theory, covering fundamental groups, Whitehead brackets, and Quillen's theorem in this advanced mathematics seminar.
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18 Lesons
1 hour 1 minute
On-Demand
Free-Video
Institute for Advanced Study

Drinfeld's Lemma for Schemes - Kiran Kedlaya

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Explore Drinfeld's lemma for schemes with Kiran Kedlaya, covering fundamental groups, base points, and the Stax project in algebraic geometry.
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10 Lesons
58 minutes
On-Demand
Free-Video
Institute for Advanced Study

Exceptional Splitting of Reductions of Abelian Surfaces With Real Multiplication - Yunqing Tang

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Explore real multiplication in abelian surfaces, focusing on exceptional splitting of reductions. Delve into simple reduction, finite extension, and density zero concepts with insights on special devices and intersection numbers.
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18 Lesons
1 hour 1 minute
On-Demand
Free-Video
Institute for Advanced Study

A Derived Hecke Algebra in the Context of the Mod P Langlands Program - Rachel Ollivier

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Explore derived Hecke algebras in mod p Langlands program, covering super singular modules, involution, trace maps, and twisted duals with Rachel Ollivier.
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9 Lesons
56 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Relative Poincaré Duality in Non Archimedean Geometry

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Delve into advanced mathematical concepts exploring relative mod-p Poincaré duality in rigid-analytic varieties, featuring novel trace map constructions and diagrammatic proofs for smooth morphisms.
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1 Lesons
1 hour 9 minutes
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Free-Video
Applied Algebraic Topology Network

Optimal Topological Simplification of Surfaces

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Algorithmes et résultats de complexité pour simplifier la topologie des surfaces de manière optimale, en utilisant des courbes et graphes les plus courts possible.
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11 Lesons
47 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Stability of Reeb Ordering Method in the Framework of Pospaces

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Explores stability of Reeb ordering in pospaces, introducing new tools for manipulating posets as graph-like objects and proving stability using interleaving distance among order-compatible topological spaces.
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1 Lesons
46 minutes
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Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Paires de Hecke et K-théorie

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Explorez les paires de Hecke en théorie des nombres, leur lien avec la géométrie à grande échelle et les applications aux conjectures de Baum-Connes et Novikov. Découvrez les avancées en K-théorie des C*-algèbres de Hecke.
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1 Lesons
45 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

The Completion of the Space of Lagrangian Submanifolds for the Spectral Metric

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Explore the spectral metric on Lagrangian spaces, its completion, and connections to symplectic topology and sheaf theory through quantization.
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1 Lesons
48 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
On-Demand
Free-Video
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

0 rewiews
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
On-Demand
Free-Video
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
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Grupo Fundamental e Espaços de Recobrimento - Aula 06

0 rewiews
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
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Grupo Fundamental e Espaços de Recobrimento - Aula 22

0 rewiews
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
On-Demand
Free-Video
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
On-Demand
Free-Video
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
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Grupo Fundamental e Espaços de Recobrimento - Aula 19

0 rewiews
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
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Grupo Fundamental e Espaços de Recobrimento - Aula 12

0 rewiews
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
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Grupo Fundamental e Espaços de Recobrimento - Aula 11

0 rewiews
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 10

0 rewiews
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

0 rewiews
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
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Grupo Fundamental e Espaços de Recobrimento - Aula 16

0 rewiews
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

0 rewiews
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

0 rewiews
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

0 rewiews
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
Banach Center

Leray Functor in Connection Matrices

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Explore the Leray Functor's role in connection matrices, delving into advanced mathematical concepts and their applications in topology and algebra.
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1 Lesons
16 minutes
On-Demand
Free-Video
Banach Center

Euler Characteristic Curves and Profiles

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Explore Euler Characteristic Curves and Profiles in topological data analysis, gaining insights into shape analysis and data visualization techniques.
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1 Lesons
30 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Hyperbolization, Cubulation, and Applications in Negative Curvature Geometry

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Explore hyperbolization procedures, their impact on polyhedra, and the resulting manifolds' properties. Discover how fundamental groups interact with CAT(0) cube complexes in negatively curved spaces.
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1 Lesons
55 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

The Isomorphism Problem for Artin Groups

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Explorez le problème d'isomorphisme pour les groupes d'Artin, en particulier pour les groupes de "grand type". Découvrez les défis, les conjectures et les résultats partiels dans ce domaine mathématique complexe.
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1 Lesons
58 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Spaces of Orderings and Applications - Lecture 4

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Explore the topology of orderable group spaces, their properties, and connections to group algebra. Discuss open questions in this mathematical field.
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1 Lesons
49 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Spaces of Orderings and Applications - Lecture 3

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Explore the topology of orderable group spaces, their properties, and connections to group algebra. Discuss open questions in this mathematical field.
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1 Lesons
46 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Heisenberg Homology of Surface Configurations

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Explore Heisenberg group representations on surface configurations, examining homologies, Mapping Class Group actions, and quantum connections in mathematical research.
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1 Lesons
49 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Algebraization of Low-Dimensional Topology - Lecture 4

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Explore algebraic presentations of cobordism categories in 3 and 4 dimensions, focusing on torus-based structures and their implications for Topological Quantum Field Theories.
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1 Lesons
57 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Algebraization of Low-Dimensional Topology - Part I

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Explore algebraic presentations of cobordism categories in low-dimensional topology. Learn about 3- and 4-modular Hopf algebras and their role in classifying TQFTs.
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1 Lesons
57 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Khovanov-Seidel Braids Representation

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Explore Khovanov-Seidel braids representation in this mathematical conference talk. Gain insights into current trends in representation theory, cluster algebras, and geometry.
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1 Lesons
55 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Torsion Volume Forms

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Explore torsion volume forms in algebraic geometry and topology with Pavel Safronov's in-depth mathematical analysis and insights.
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1 Lesons
58 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Algebraic Approximation of Submanifolds of Real Algebraic Varieties

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Explore algebraic approximation of submanifolds in real algebraic varieties with Olivier Benoist. Gain insights into advanced mathematical concepts and their applications in geometry.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

The Humilière Completion and Its Applications in Symplectic Geometry

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Explore the Humilière completion of Lagrangian spaces, its spectral distance study, and applications in conformal dynamics, singular Hamiltonian systems, and sheaf theory.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Perfect Kernels and Dynamics: From Bass-Serre Theory to Hyperbolic Groups

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Explore perfect kernels and dynamics in mathematics, from Bass-Serre theory to hyperbolic groups, with insights from Pénélope Azuelos's conference talk at CIRM.
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1 Lesons
46 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Random Walks on Simplicial Complexes

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Explore random walks on simplicial complexes in this mathematical conference talk, delving into advanced concepts and applications in the field.
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1 Lesons
55 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Grupo Fundamental e Espaços de Recobrimento - Aula 03

0 rewiews
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
Free-Video
Instituto de Matemática Pura e Aplicada

Teoria de Hodge: Variedade de Fermat I - Aula 17

0 rewiews
Explore a Teoria de Hodge aplicada à variedade de Fermat, aprofundando-se em conceitos avançados de geometria algébrica e topologia.
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1 Lesons
53 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Teoria de Hodge: Gauss-Manin Connection - Aula 16

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Explore a conexão de Gauss-Manin na Teoria de Hodge, aprofundando-se em conceitos avançados de matemática pura aplicada ao doutorado.
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1 Lesons
55 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Teoria de Hodge: Hodge Loci - Aula 19

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Explore Hodge loci in advanced mathematics, delving into complex algebraic geometry and Hodge theory concepts for doctoral-level understanding.
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1 Lesons
1 hour 8 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Teoria de Hodge da Variedade de Fermat - Aula 18

0 rewiews
Explore a Teoria de Hodge aplicada à variedade de Fermat, aprofundando-se em conceitos avançados de geometria algébrica e topologia.
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1 Lesons
59 minutes
On-Demand
Free-Video
Models of Consciousness Conferences

Neural Sense Relations and Consciousness - A Diagrammatic Approach

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Explores neural sense relations and consciousness through inversion symmetry, proposing a topological model linking subject-object domains in brain function, with implications for understanding subjective experience.
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14 Lesons
23 minutes
On-Demand
Free-Video
Models of Consciousness Conferences

Making Up Our Minds

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Explore how minds and thoughts are constructed through cognitive processes, examining the nature of consciousness, memory, and perception using interdisciplinary models and mathematical frameworks.
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7 Lesons
13 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Perverse Sheaves and Resurgence in Borel Summation

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Explore the connection between resurgence theory and perverse sheaves, focusing on Borel summation, Stokes phenomena, and alien derivatives in algebraic structures.
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1 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Stabilizing the Unstable Output of Persistent Homology Computations

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Explore stabilizing techniques for persistent homology computations, focusing on generating cycles and their applications in topological data analysis.
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19 Lesons
44 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Sampling Smooth Manifolds Using Ellipsoids

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Explore sampling smooth manifolds using ellipsoids, a novel approach requiring lower sample density than traditional ball-based methods, with potential applications in data science and topology.
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9 Lesons
46 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Alexander Wagner - Nonembeddability of Persistence Diagrams into Hilbert Spaces

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Explore nonembeddability of persistence diagrams in Hilbert spaces, examining stability, metrics, and implications for machine learning applications in topological data analysis.
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10 Lesons
27 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Computing Persistent Homology - Introduction

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Explore the fundamentals of persistent homology computation, covering key concepts, intuition, and practical applications in topological data analysis.
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7 Lesons
27 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Conley-Morse-Forman Theory for Generalized Combinatorial Multivector Fields

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Generalized combinatorial multivector fields on finite topological spaces: extending Conley-Morse-Forman theory for data science applications, including isolated invariant sets, Conley index, and Morse decompositions.
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11 Lesons
26 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Ulrich Bauer - Persistence Diagrams as Diagrams

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Explore persistence diagrams as categorical functors, examining their structure, stability, and relationships to matchings. Learn about new constructions and theorems in this advanced algebraic topology lecture.
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19 Lesons
1 hour 9 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Vanessa Robins - Persistence Diagrams of Bead Packings

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Exploring grain-scale mechanisms in granular crystallization using X-ray tomography and persistent homology, revealing key formation processes of tetrahedral and octahedral pores in spherical bead packings.
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15 Lesons
51 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Nonlinear Dynamics, High Dimensional Data, and Persistent Homology

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Explore nonlinear dynamics, high-dimensional data analysis, and persistent homology with Konstantin Mischaikow. Learn about algebraic topology applications, persistence diagrams, and recent advancements in data science.
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18 Lesons
1 hour 9 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Gunnar Carlsson - Local to Global Principles in Persistent Homology

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Explore persistent homology's local-to-global principles, computational methods, and applications in topology and data analysis with expert Gunnar Carlsson.
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23 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

From Persistent Homology to Machine Learning

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Overview of persistent homology's applications in machine learning, exploring its use in analyzing global topology and local geometry of datasets, with examples from various fields and discussions on stability and interpretability.
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16 Lesons
29 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Invariants for Tame Parametrised Chain Complexes

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Explore invariants for tame parametrised chain complexes in applied algebraic topology, focusing on explicit constructions, comprehensive frameworks, and discriminative power in topological data analysis.
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13 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Why Should Q=P in the Wasserstein Distance Between Persistence Diagrams?

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Explore Wasserstein distance in persistence diagrams, focusing on q=p choice. Covers geometric implications, stability results, algebraic versions, and computational advantages for central tendencies.
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21 Lesons
1 hour 4 minutes
On-Demand
Free-Video
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

Persistence in Functional Topology

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Explore functional topology's evolution, connecting persistent homology to critical point theory and calculus of variations. Gain insights into Morse's theory and its application to minimal surfaces.
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15 Lesons
1 hour 5 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Conversation on the Paper "Persistent Extension and Analogous Bars" by Yoon, Ghrist, Giusti

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Explore persistent homology extensions and analogous bars in topological data analysis, discussing novel methods for comparing persistence barcodes and their applications in data science.
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16 Lesons
52 minutes
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

Other Persistence Invariants - Homotopy and the Cohomology Ring

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Explore persistent homotopy groups and cohomology rings, focusing on fundamental groups, rational homotopy, and cup-length diagrams. Learn about new tools complementing persistent homology in topological data analysis.
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13 Lesons
45 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Massimo Ferri - Selection of Points in Persistence Diagrams

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Explore point selection in persistence diagrams, including Kurlin's criterion and the Ziqqurat method, for noise reduction and improved data analysis in topological data analysis.
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9 Lesons
40 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

On Characterizing Rare Events in Persistent Homology

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Explore rare events in persistent homology, focusing on indecomposables in multi-parameter settings. Learn about large deviation principles and laws of large numbers in topological data analysis.
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17 Lesons
53 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Star Clusters in Clique Complexes and the Vietoris-Rips Complex of Planar Sets

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Explore star clusters in simplicial complexes and their applications to independence complexes and Vietoris-Rips complexes of planar sets, with insights on homotopy information and related conjectures.
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11 Lesons
50 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Vietoris-Rips Complexes of Hypercube Graphs

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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.
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8 Lesons
34 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Approximation of Compact Metric Spaces by Finite Samples

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Explore topological data analysis through finite approximations of compact metric spaces, connecting Shape Theory and Persistence for robust feature extraction from noisy datasets.
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15 Lesons
48 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Discrete Homotopy Theory and Applications

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Explore discrete homotopy theory's evolution, applications in topology, geometry, and group theory. Learn simplified approaches to fundamental groups and covering spaces, with insights into various mathematical domains.
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35 Lesons
49 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Barbara Giunti - Average Complexity of Barcode Computation for Vietoris-Rips Filtrations

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Explore algorithmic complexity of persistent homology in random Vietoris-Rips filtrations, focusing on boundary matrix fill-up and its implications for computational efficiency.
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10 Lesons
52 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Minimal Cycle Representatives in Persistent Homology Using Linear Programming

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Explores optimization techniques for selecting minimal cycle representatives in persistent homology, comparing effectiveness and computational costs of various algorithms using linear programming methods.
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1 Lesons
50 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

The Directional Transform

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

A Topological Study of the Space of Planar Pentagons

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Exploring topology of planar pentagons as a model for molecular conformation spaces, using topological data analysis for dimensionality reduction and visualization.
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1 Lesons
35 minutes
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Free-Video
Applied Algebraic Topology Network

Persistent Cycle Registration and Topological Bootstrap

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Novel approach for comparing persistent homology representations, utilizing spatial placement of persistent cycles. Demonstrates application in topological inference to differentiate signal from noise in point cloud data.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Swap, Shift and Trim to Edge Collapse a Flag Filtration

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Exploring efficient algorithms for reducing flag filtrations in persistent homology, with focus on edge collapse techniques and their applications in computational topology.
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1 Lesons
44 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

The Generalized Persistence Diagram Encodes the Bigraded Betti Numbers

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Explore how generalized persistence diagrams encode bigraded Betti numbers in 2-parameter persistence modules, with implications for RIVET software and interval decomposable modules.
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1 Lesons
39 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Topological Time Series Analysis for Hurricanes and Dynamical Systems

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Explore topological data analysis applications in studying hurricane satellite imagery and dynamical system bifurcations using persistent homology and zigzag persistence techniques.
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1 Lesons
56 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Homotopical Decompositions of Simplicial and Vietoris Rips Complexes

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Explore homotopical decompositions of simplicial complexes, focusing on obstruction complexes and their applications in topological data analysis, with insights on Vietoris-Rips complexes.
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1 Lesons
31 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Differential Calculus on Persistence Barcodes

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Explore differential calculus on persistence barcodes, covering differentiability concepts, lifts to ordered barcodes, and applications in topological data analysis.
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1 Lesons
29 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

On the Metric Distortion of Embedding Persistence Diagrams into RKHS

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Explores embedding Persistence Diagrams into Reproducing Kernel Hilbert Spaces, analyzing metric properties and stability guarantees for machine learning applications in Topological Data Analysis.
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1 Lesons
55 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Multiple Hypothesis Testing with Persistent Homology

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Exploring methods for multiple hypothesis testing in persistent homology, including family-wise error rates and false discovery rates, with applications to Mapper complex validation.
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1 Lesons
57 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

An Intrinsic Persistent Homology Transform

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Explores an intrinsic persistent homology transform for metric spaces, focusing on metric graphs. Discusses injectivity results and compares to related constructs in topological data analysis.
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1 Lesons
51 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Topological Data Analysis of Collective Motion

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Explore topological data analysis for collective motion in nature, examining bird flocks, fish schools, and insect swarms through innovative mathematical models and simulations.
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1 Lesons
56 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
Free-Video