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#Simplicial Complexes

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Santa Fe Institute

Topology Shapes Dynamics of Higher-order Networks

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Exploring how higher-order network interactions influence non-linear dynamics, synchronization, and percolation in complex systems like brain networks and climate patterns.
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1 Lesons
56 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
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

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
IEEE Signal Processing Society

Principled Simplicial Neural Networks for Trajectory Prediction

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Learn advanced techniques for trajectory prediction using simplicial neural networks, exploring their principles and applications in data science and signal processing.
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1 Lesons
1 hour 12 minutes
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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
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Free-Video
Applied Algebraic Topology Network

Bridging Applied and Quantitative Topology

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Survey of emerging connections between applied and quantitative topology, focusing on Vietoris-Rips complexes and their applications in computational topology, geometric group theory, and dataset shape approximation.
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1 Lesons
58 minutes
On-Demand
Free-Video
Insights into Mathematics

Computing Homology Groups - Algebraic Topology - NJ Wildberger

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Explore homology groups in algebraic topology, focusing on examples like circles and disks. Learn about connectivity, loops, and higher-dimensional holes in spaces.
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6 Lesons
41 minutes
On-Demand
Free-Video
Insights into Mathematics

Simplices and Simplicial Complexes - Algebraic Topology

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Explore higher-dimensional geometry through simplices and simplicial complexes. Learn about convex combinations, orientations, and the fundamental concept of homology in algebraic topology.
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8 Lesons
49 minutes
On-Demand
Free-Video
Paul G. Allen School

Theory Seminar - Face Numbers, Isabella Novik

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Face numbers in centrally symmetric polytopes and spheres: exploring upper bounds, recent developments, and open problems in combinatorial geometry. Insights into maximum face counts and structural properties.
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9 Lesons
55 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Decomposing Simplicial Complexes - Without Losing Pieces

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Explore simplicial complex decomposition, its impact on homotopy type, and applications in Vietoris-Rips complexes. Learn about obstruction complexes and their role in understanding topological changes.
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9 Lesons
48 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Simplicial Neural Networks

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Explore simplicial neural networks, a generalization of graph neural networks for multi-dimensional data, and their applications in imputing missing data on coauthorship complexes.
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10 Lesons
52 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

The Topological Dirac Operator and the Dynamics of Topological Signals

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Explore topological signals, higher-order Laplacians, and the Dirac operator in network science. Learn about spectral properties, diffusion dynamics, and topological synchronization in simplicial complexes and multiplex networks.
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25 Lesons
53 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Sheaf Based Modeling of Wireless Communications

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Explore sheaf-based modeling for wireless communications, covering topology, simplicial complexes, interference, and network activation. Learn about persistence, homological invariants, and simulation examples.
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26 Lesons
57 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

What's Behind the Homotopical Decomposition of a Simplicial Complex

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Explore homotopical decomposition of simplicial complexes, focusing on conditions for homotopy type preservation and the mathematics behind decomposability results.
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10 Lesons
48 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Dejan Govc - Fundamental Groups of Small Simplicial Complexes

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Explore minimal triangulations of manifolds and fundamental groups of small simplicial complexes, with insights on estimating vertex counts in minimal triangulations.
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8 Lesons
47 minutes
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Free-Video
Applied Algebraic Topology Network

Borsuk–Ulam Theorems for Maps into Higher-Dimensional Codomains

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Explore Borsuk-Ulam theorems for sphere maps to higher-dimensional spaces, examining topological properties and optimal diameter bounds for odd maps from S^n to R^k where k > n.
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1 Lesons
42 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Efficient Approximation of the Matching Distance for 2-Parameter Persistence

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Explore efficient algorithms for approximating matching distance in 2-parameter persistence modules, focusing on quad-tree refinement and local adaptive bounds for improved computational performance.
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1 Lesons
30 minutes
On-Demand
Free-Video
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
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Free-Video
Applied Algebraic Topology Network

Yevgeny Liokumovich - Urysohn Width, Isoperimetric Inequalities and Scalar Curvature

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Explore metric spaces, Hausdorff measure, and continuous mappings. Discover connections to isoperimetric inequalities and Riemannian geometry's positive scalar curvature.
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1 Lesons
49 minutes
On-Demand
Free-Video
ICTP Mathematics

Topology - Lecture 13

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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 33 minutes
On-Demand
Free-Video
ICTP Mathematics

Topology - Lecture 20

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Explore advanced concepts in topology, including complex mathematical structures and their properties, in this comprehensive lecture by Bruno Zimmerman.
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1 Lesons
1 hour 38 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 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 16

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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 35 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
Applied Algebraic Topology Network

Urysohn Width

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Explore the 100-year history and applications of Urysohn width, a metric invariant quantifying space approximation by simplicial complexes. Discover its role in dimension theory and modern geometric challenges.
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1 Lesons
54 minutes
On-Demand
Free-Video
Simons Institute

High-Dimensional Expanders - Lecture 1

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Explore high-dimensional expanders with Irit Dinur, delving into advanced concepts in analysis and theoretical computer science.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Simons Institute

High-Dimensional Expanders - Lecture 4

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Explore advanced concepts in high-dimensional expanders, focusing on analysis techniques and applications in theoretical computer science.
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1 Lesons
1 hour 7 minutes
On-Demand
Free-Video
Simons Institute

High-Dimensional Expanders - Lecture 3

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Explore advanced concepts in high-dimensional expanders, focusing on analysis techniques and applications in theoretical computer science.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Simons Institute

Higher-Dimensional Expansion of Random Geometric Complexes

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Explores 2-dimensional spectral expansion in hypergraphs, demonstrating that triangles in high-dimensional random geometric graphs form expanding simplicial complexes of low polynomial degree.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Society for Industrial and Applied Mathematics

Random Monomial Ideals - Seminar on Applied Geometry and Algebra

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Explore probabilistic models of random monomial ideals, their properties, and applications in algebraic geometry. Gain insights into average behavior of ideals and potential for generating algebraic objects.
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1 Lesons
46 minutes
On-Demand
Free-Video
Insights into Mathematics

Delta Complexes, Betti Numbers, and Torsion in Algebraic Topology

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Explore homology groups of torus and projective plane using delta-complexes. Learn about Betti numbers and torsion in algebraic topology, with practical computations and insights into fundamental concepts.
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1 Lesons
48 minutes
On-Demand
Free-Video
IMSA

Simplicial Complexes and Face Rings - January 29, 2024

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Explore simplicial complexes and face rings, including stars and links, and their correspondence in Stanley-Reisner rings. Gain insights into fundamental concepts of algebraic topology.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
IMSA

Anisotropy, Biased Pairings and the Lefschetz Property - January 30, 2024

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Explore anisotropy in face rings of simplicial spheres, biased pairing property, and Hall-Laman relations. Discover their connections to the Lefschetz property in advanced mathematics.
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1 Lesons
47 minutes
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Classical Topology and Quantum Complexity - IPAM at UCLA

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Explore the intersection of classical topology and quantum complexity, focusing on computational challenges in determining homology groups and their implications for quantum mechanics and data analysis.
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1 Lesons
54 minutes
On-Demand
Free-Video
Fields Institute

Loop Space Decompositions of Moment-Angle Complexes Associated to Flag Complexes and Low Dimensional Simplicial Complexes

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Explore loop space decompositions of moment-angle complexes, focusing on flag complexes and low-dimensional simplicial complexes in this advanced topology talk.
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1 Lesons
40 minutes
On-Demand
Free-Video
Fields Institute

Remarks on the Combinatorial Topology of Moment-Angle Complexes

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Explore combinatorial topology of moment-angle complexes with Sergio Chaves, delving into advanced mathematical concepts and their applications in toric topology and geometry.
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1 Lesons
41 minutes
On-Demand
Free-Video
Fields Institute

The Resonance Schemes of Simplicial Complexes

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Explore resonance schemes of simplicial complexes in this advanced mathematics talk by Alexandru Suciu, delving into toric topology and polyhedral products.
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1 Lesons
49 minutes
On-Demand
Free-Video
Fields Institute

On the Moment-Angle Manifolds Over Bier Spheres

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Explore moment-angle manifolds over Bier spheres in this mathematical talk, delving into advanced concepts in toric topology and polyhedral products.
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1 Lesons
44 minutes
On-Demand
Free-Video
Fields Institute

Polyhedral Products in Motivic Homotopy Theory

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Explore polyhedral products in motivic homotopy theory, delving into advanced mathematical concepts and their applications in algebraic topology and geometry.
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1 Lesons
47 minutes
On-Demand
Free-Video
Fields Institute

Steenrod's Problem for Face Rings

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Explore Steenrod's Problem in face rings, delving into advanced algebraic topology concepts and their applications in toric topology and polyhedral products.
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1 Lesons
44 minutes
On-Demand
Free-Video
Fields Institute

A Generalization of Polyhedral Products

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Explore advanced concepts in algebraic topology, focusing on a novel generalization of polyhedral products and their applications in toric topology and geometry.
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1 Lesons
52 minutes
On-Demand
Free-Video
Fields Institute

Flag Complexes, Polyhedral Products and Geometric Group Theory

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Explore connections between flag complexes, polyhedral products, and geometric group theory in this advanced mathematics lecture by Stephen Theriault from the University of Southampton.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Fields Institute

Properties of Polyhedral Products

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Explore properties of polyhedral products in this advanced mathematics lecture, covering key concepts and applications in toric topology and geometry.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Fields Institute

The Davis-Januszkiewicz Construction Reinterpreted and Generalized

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Explore a reinterpretation and generalization of the Davis-Januszkiewicz construction in toric topology, presented by Anthony Bahri from Rider University as part of the Graduate School on Toric Topology.
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1 Lesons
1 hour 21 minutes
On-Demand
Free-Video
Fields Institute

An Introduction to Polyhedral Products

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Explore the foundations of polyhedral products in this graduate-level lecture, covering key concepts and applications in toric topology and geometry.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video
ICTP Condensed Matter and Statistical Physics

Topology and Dynamics of Higher-Order Networks - Lecture 1: General Introduction to Algebraic Topology on Networks and Simplicial Complexes

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Explore algebraic topology in networks and simplicial complexes, focusing on homology and boundary operators. Gain insights into higher-order network structures and their impact on complex systems.
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1 Lesons
2 hours 16 minutes
On-Demand
Free-Video
ICTP Condensed Matter and Statistical Physics

Topology and Dynamics of Higher-Order Networks - Lecture 2: Introduction to Algebraic Topology on Networks and Simplicial Complexes

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Explore algebraic topology on networks and simplicial complexes, focusing on Hodge Laplacians and Dirac operators in higher-order networks. Gain insights into topological signals and their applications.
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1 Lesons
2 hours
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Multiscale Basis Dictionaries and Scattering Networks on Simplicial Complexes

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Explore multiscale basis dictionaries and scattering networks on simplicial complexes, focusing on HGLET and GHWT. Learn applications in coauthorship/citation complex and article classification.
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1 Lesons
34 minutes
On-Demand
Free-Video
Stony Brook Mathematics

The High-Degree Rational Cohomology of the Special Linear Group

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Explore high-degree rational cohomology of SL_n(Z) and SL_n(R) for number rings. Examine Steinberg modules and associated simplicial complexes to understand special linear group cohomology.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Waists Measured via Urysohn Width in Riemannian Manifolds

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Explore Urysohn width's role in measuring approximate dimension of Riemannian manifolds and its connection to positive scalar curvature, with insights on slicing manifolds.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Banach Center

L^2 Cohomology of Buildings

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Explore L^2 cohomology of buildings with Tadeusz Januszkiewicz, delving into advanced mathematical concepts and their applications in geometric group theory.
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1 Lesons
1 hour 10 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

L^2 Homology of Groups and Consequences - Part I

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Explore l^2 homology of groups, its definition via simplicial complex actions, and implications for group theory, particularly when these invariants vanish.
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1 Lesons
54 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

L^2 Homology of Groups and Consequences - Lecture 3

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Explore l^2 homology of groups, its computation, and implications for group theory, focusing on cases where these invariants vanish.
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1 Lesons
47 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

L^2 Homology of Groups and Consequences - Lecture 2

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Explore l^2 homology of groups through examples, calculations, and implications for group theory, focusing on vanishing invariants.
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1 Lesons
53 minutes
On-Demand
Free-Video
BIMSA

Triangulations of Manifolds and the Triangulation Conjecture

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Explore the triangulation conjecture in topology, its validity in low dimensions, and its disproval in higher dimensions using advanced mathematical techniques.
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1 Lesons
49 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Homology of Graphs and Hypergraphs

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Explore topological structures of graphs and hypergraphs, including recent findings on homology and persistent homology, with applications in combinatorial and metric space analysis.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Discover AI

Topological Message Passing: From Graph Neural Networks to Simplicial Complexes on CW Networks

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Delve into advanced Graph Neural Network concepts, exploring topological message passing, simplicial complexes, and high-dimensional interactions for computational graph networks and molecular design applications.
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1 Lesons
25 minutes
On-Demand
Free-Video
Simons Institute

High-Dimensional Expanders - Lecture 2

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Explore high-dimensional expanders with Irit Dinur, delving into advanced concepts and applications in analysis and theoretical computer science.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
IMSA

Low Dimensional Topology and Circle-Valued Morse Functions

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Explore the Kakimizu complex for genus one hyperbolic knots, examining its structure, dimensions, and examples across various dimensions in 3-sphere topology.
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21 Lesons
54 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Interactions and Topological Synchronization in Simplicial Kuramoto Model

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Delve into the mathematical foundations of simplicial Kuramoto models, exploring oscillator dynamics, topology-geometry relationships, and synchronization patterns in complex networks.
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1 Lesons
43 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Persistent Homology of Plant-Pollinator Interactions - The Importance of Flowering Plant Surveys

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Explore persistent homology in plant-pollinator interactions, analyzing topological features and the impact of flowering plant surveys on understanding community structures.
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1 Lesons
46 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Computing Generalized Ranks of Persistence Modules via Unfolding to Zigzag Modules

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Efficient algorithm for computing generalized ranks of persistence modules using unfolding to zigzag modules, with applications in algebraic topology and data analysis.
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1 Lesons
46 minutes
On-Demand
Free-Video
Dublin Institute for Advanced Studies DIAS

Quantum Finite Elements: The Affine Projection for Lattice Field Theory on Curved Manifolds

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Explore quantum finite elements and affine projections for lattice field theory on curved manifolds, focusing on Ising conformal field theory applications and potential extensions.
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1 Lesons
1 hour 58 minutes
On-Demand
Free-Video
Institute for Advanced Study

Local-to-Global Theorems on High Dimensional Expanders

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Explore high dimensional expansion theory, from graph fundamentals to complex applications in error-correcting codes and PCPs, focusing on how local properties influence global behaviors in mathematical structures.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Homotopy and Singular Homology Groups of Finite Digraphs

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Explore advanced algebraic topology concepts through the computation of homotopy and singular homology groups in finite directed graphs, with applications in data analysis and network science.
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1 Lesons
48 minutes
On-Demand
Free-Video
Institute for Advanced Study

The Schubert Variety of a Pair of Linear Spaces

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Delve into advanced mathematical concepts exploring Schubert varieties, Kempf collapsing, and matroid theory through the lens of linear spaces and their geometric relationships.
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1 Lesons
1 hour 7 minutes
On-Demand
Free-Video