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Simplicial Complexes

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Explore algebraic topology through simplicial complexes, learning decomposition methods, face numbers, and higher-dimensional network analysis. Access research seminars and tutorials on YouTube from leading mathematics institutes, covering applications in topological deep learning and simplicial neural networks.

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Applied Algebraic Topology Network
Decomposing Simplicial Complexes - Without Losing Pieces

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.
- YouTube
- 48 minutes
- On-Demand
- Free Video
Fields Institute
The Resonance Schemes of Simplicial Complexes

Explore resonance schemes of simplicial complexes in this advanced mathematics talk by Alexandru Suciu, delving into toric topology and polyhedral products.
- YouTube
- 49 minutes
- On-Demand
- Free Video
Fields Institute
Simplicial Complexes with Many Facets Are Vertex Decomposable

Explore the concept of vertex decomposability in simplicial complexes with numerous facets in this mathematical research presentation by Ritika Nair.
- YouTube
- 22 minutes
- On-Demand
- Free Video
Valence Labs
Topological Deep Learning: Going Beyond Graph Data

Explore topological deep learning for data on complex domains. Learn about message passing, neighborhood functions, and combinatorial complex neural networks for advanced machine learning applications.
- YouTube
- 1 hour 3 minutes
- On-Demand
- Free Video
Applied Algebraic Topology Network
Simplicial Neural Networks

Explore simplicial neural networks, a generalization of graph neural networks for multi-dimensional data, and their applications in imputing missing data on coauthorship complexes.
- YouTube
- 52 minutes
- On-Demand
- Free Video
Applied Algebraic Topology Network
The Topological Dirac Operator and the Dynamics of Topological Signals

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.
- YouTube
- 53 minutes
- On-Demand
- Free Video
Applied Algebraic Topology Network
Urysohn Width

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.
- YouTube
- 54 minutes
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- Free Video
Simons Institute
Higher-Dimensional Expansion of Random Geometric Complexes

Explores 2-dimensional spectral expansion in hypergraphs, demonstrating that triangles in high-dimensional random geometric graphs form expanding simplicial complexes of low polynomial degree.
- YouTube
- 1 hour 4 minutes
- On-Demand
- Free Video
Paul G. Allen School
Theory Seminar - Face Numbers, Isabella Novik

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.
- YouTube
- 55 minutes
- On-Demand
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Insights into Mathematics
Simplices and Simplicial Complexes - Algebraic Topology

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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- 49 minutes
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Discover AI
Topological Message Passing: From Graph Neural Networks to Simplicial Complexes on CW Networks

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.
- YouTube
- 25 minutes
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Applied Algebraic Topology Network
Homotopical Decompositions of Simplicial and Vietoris Rips Complexes

Explore homotopical decompositions of simplicial complexes, focusing on obstruction complexes and their applications in topological data analysis, with insights on Vietoris-Rips complexes.
- YouTube
- 31 minutes
- On-Demand
- Free Video
Applied Algebraic Topology Network
Dejan Govc - Fundamental Groups of Small Simplicial Complexes

Explore minimal triangulations of manifolds and fundamental groups of small simplicial complexes, with insights on estimating vertex counts in minimal triangulations.
- YouTube
- 47 minutes
- On-Demand
- Free Video
Institut des Hautes Etudes Scientifiques (IHES)
Multiscale Basis Dictionaries and Scattering Networks on Simplicial Complexes

Explore multiscale basis dictionaries and scattering networks on simplicial complexes, focusing on HGLET and GHWT. Learn applications in coauthorship/citation complex and article classification.
- YouTube
- 34 minutes
- On-Demand
- Free Video
Fields Institute
Loop Space Decompositions of Moment-Angle Complexes Associated to Flag Complexes and Low Dimensional Simplicial Complexes

Explore loop space decompositions of moment-angle complexes, focusing on flag complexes and low-dimensional simplicial complexes in this advanced topology talk.
- YouTube
- 40 minutes
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