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#Applied Algebraic Topology

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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

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
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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
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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

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

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
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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

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

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
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Free-Video
Applied Algebraic Topology Network

Ippei Obayashi - Stable Volumes for Persistent Homology

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Explore stable volumes in persistent homology: a novel method to identify robust topological structures in data, overcoming instability issues and revealing minimal building blocks.
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1 Lesons
54 minutes
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Free-Video
Applied Algebraic Topology Network

Multi-Parameter Persistent Homology is Practical

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Explore practical applications of multi-parameter persistent homology in topological data analysis, focusing on efficient algorithms for large datasets and recent computational advancements.
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1 Lesons
1 hour 6 minutes
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Free-Video
Applied Algebraic Topology Network

Parallel Decomposition of Persistence Modules Through Interval Bases

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Explore parallel decomposition of persistence modules using interval bases, enhancing Topological Data Analysis with distributed computation and Hodge decomposition techniques.
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1 Lesons
50 minutes
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Free-Video
Applied Algebraic Topology Network

The Persistence Mayer-Vietoris Spectral Sequence

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Explore the persistent Mayer-Vietoris spectral sequence, its applications in parallelizing persistent homology computations, and its ability to provide locality-enriched persistence barcodes.
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1 Lesons
51 minutes
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Free-Video
Hausdorff Center for Mathematics

Novel Computational Perspectives of Persistence

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Explore innovative computational approaches to persistence in algebraic topology, focusing on advanced techniques and their applications in data analysis and topological research.
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1 Lesons
54 minutes
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Free-Video
Applied Algebraic Topology Network

Greg Malen - Collapsibility of Random Clique Complexes

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Explore k-collapsibility in random clique complexes, examining dimensional faces, strong connectivity, and homology implications for topological data analysis.
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15 Lesons
55 minutes
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Free-Video
Applied Algebraic Topology Network

Solving Systems of ODEs via Combinatorial Homological Algebra

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Exploring efficient computation of homological representations in dynamical systems, with applications to differential equations and parameter space analysis.
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10 Lesons
52 minutes
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Free-Video
Applied Algebraic Topology Network

Topological Complexity Using Arbitrary Covers

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

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

Luis Scoccola - Locally Persistent Categories & Metric Properties of Interleaving Distances

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Explore locally persistent categories, metric properties of interleaving distances, and their applications in algebraic topology, including natural interleavings and weak equivalences.
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9 Lesons
31 minutes
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Free-Video
Applied Algebraic Topology Network

Nathanael Cox - Effective Algorithms for Quotients of Semi-Algebraic Equivalence Relations

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Explore efficient algorithms for computing quotients of semi-algebraic equivalence relations, focusing on complexity, tools, and key results in applied algebraic topology.
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7 Lesons
26 minutes
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Free-Video
Applied Algebraic Topology Network

Takashi Owada - Limit Theorems for Topological Invariants of the Dynamic Multi-Parameter Simplicial Complex

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Explore topological invariants in dynamic multi-parameter simplicial complexes, covering connectivity, probability, and limiting processes in applied algebraic topology.
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15 Lesons
28 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Vanessa Robins Interviewed by Elizabeth Bradley

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Explore applied topology with Vanessa Robins as she discusses her career journey, research interests, and insights on granular materials, collaborations, and emerging areas in the field.
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21 Lesons
50 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Tamal Dey - A Framework for Topological Summarization

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Explore topological summarization frameworks, covering concepts like nerve complexes, multiscale mapper, persistence diagrams, and stability in hierarchical covers. Gain insights into advanced computational topology techniques.
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17 Lesons
57 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Omer Bobrowski - Maximally Persistent Cycles in Random Geometric Complexes

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Explore persistent cycles in random geometric complexes, examining key tools, processes, and results. Gain insights into random graph theory and future research directions.
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17 Lesons
1 hour
On-Demand
Free-Video
Applied Algebraic Topology Network

Applied Algebraic Topology Network - Student Seminar Introduction to JavaPlex

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Learn to use JavaPlex for topological data analysis, covering key concepts like witness complexes, data representation, and visualization tools. Ideal for students exploring computational topology.
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19 Lesons
59 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Benjamin Schweinhart - Statistical Topology of Random Cell Complexes, and Applications

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Explore statistical topology of random cell complexes, covering curvature flow, grain growth, graph limits, and computational evidence for steady state hypothesis.
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17 Lesons
59 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Farzana Nasrin - Random Persistence Diagram Generator

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Explore a method for generating random persistence diagrams using parametric models and Markov chain Monte Carlo algorithms, with applications in material science and topology.
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18 Lesons
53 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Emergent Network Geometry

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Explore emergent network geometry, from complex networks to quantum spacetime, revealing hidden structures and applications in diverse fields like neuroscience and collaboration networks.
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18 Lesons
43 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

Žiga Virk - Information Encoded in Persistence Diagrams

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Explore topological data analysis through persistence diagrams, uncovering spatial properties like homology, geodesics, and proximity in various mathematical contexts.
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13 Lesons
47 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Herbert Edelsbrunner Interviewed by Dmitriy Morozov - September 30, 2020

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Insightful interview with Herbert Edelsbrunner, exploring his contributions to computational geometry and topology, career journey, and perspectives on the field's evolution and future directions.
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1 Lesons
53 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
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Free-Video
Applied Algebraic Topology Network

Solving Equations and Optimization Problems with Uncertainty

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Explore algorithms for detecting zeros of imprecise continuous functions and approximating worst-case optima in optimization problems with uncertain feasible domains.
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1 Lesons
43 minutes
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Free-Video
Applied Algebraic Topology Network

Frédéric Chazal Interviewed by Steve Oudot

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Entretien approfondi avec Frédéric Chazal, pionnier de la topologie appliquée, explorant son parcours, ses contributions majeures et sa vision pour l'avenir du domaine.
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1 Lesons
1 hour 18 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Kathryn Hess Interviewed by Peter Bubenik - August 11, 2021

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Engaging interview with mathematician Kathryn Hess, exploring her research, insights, and contributions to applied algebraic topology and related fields.
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1 Lesons
57 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Cell Complex Neural Networks

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Exploring neural network computations on cell complexes, generalizing graph neural networks and introducing inter-cellular message passing schemes that consider underlying topology.
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1 Lesons
46 minutes
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Free-Video
Applied Algebraic Topology Network

Approximate and Discrete Vector Bundles

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Explore synchronization problems and dimensionality reduction through vector bundles. Learn how characteristic classes provide insights into global synchronization and data analysis challenges.
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1 Lesons
1 hour
On-Demand
Free-Video
Applied Algebraic Topology Network

Gunnar Carlsson Interviewed by Vin de Silva - February 3, 2021

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Insightful interview with Gunnar Carlsson, exploring topics in applied algebraic topology and its applications in data analysis and machine learning.
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1 Lesons
56 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Universality of Persistence Diagrams and Bottleneck & Wasserstein Distances

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Explore the mathematical foundations of persistence diagrams and their associated metrics, focusing on universality properties and distance calculations in topological data analysis.
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1 Lesons
28 minutes
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Free-Video
Applied Algebraic Topology Network

RipsNet- Fast and Robust Estimation of Persistent Homology for Point Clouds

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Estimating persistence diagrams of point clouds using neural networks for faster, more robust topological analysis. Overcomes computational complexity and sensitivity to outliers in practical applications.
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1 Lesons
54 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Claudia Landi - Multi-parameter Persistence from the Viewpoint of Discrete Morse Theory

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Explore multi-parameter persistence through discrete Morse theory, connecting combinatorial properties of critical cells to algebraic properties of persistence modules in topological data analysis.
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1 Lesons
44 minutes
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Free-Video
Applied Algebraic Topology Network

Linear Obstacles in Linear Systems and Ways to Avoid Them

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Explore topology in control theory, focusing on obstacle-avoiding paths and cohomology rings using homotopy limits. Gain insights into theoretical computer science applications.
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1 Lesons
47 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Robert Adler Interviewed by Omer Bobrowski

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Insightful interview exploring Robert Adler's contributions to applied algebraic topology, offering valuable perspectives on the field's development and future directions.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Enabling a Machine to Sense Geometry

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Explore how to construct a reach space of kernels on persistent modules, enabling machine intelligence to sense geometry, with applications in synthetic and real scenarios.
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1 Lesons
51 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

The Intrinsic Volumes of a Space Filling Diagram and Their Derivatives

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Explore intrinsic volumes in molecular dynamics, focusing on space-filling diagrams and their derivatives. Learn formulas for weighted volumes and curvatures in Alpha shape representations.
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1 Lesons
50 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Stratified Covering Maps and Interleavings

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Explore stratified covering maps and interleavings in algebraic topology, examining their applications and theoretical foundations.
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1 Lesons
59 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Descriptive Geometry of Function Spaces

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Explore the intricate world of function spaces and their descriptive geometry in this advanced mathematical lecture by Shmuel Weinberger, part of the Hausdorff Trimester Program.
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1 Lesons
53 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Natural Homology Computability and Eilenberg Steenrod Axioms

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Explore natural homology computability and Eilenberg Steenrod axioms in this advanced mathematics lecture, delving into applied and computational algebraic topology concepts.
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1 Lesons
48 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Poisson U Statistics Subgraph and Component Counts in Random Geometric Graphs

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Explore Poisson U statistics, subgraph counts, and component analysis in random geometric graphs, advancing knowledge in applied algebraic topology.
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1 Lesons
47 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

A Sheaf-based Approach to Graph Neural Networks

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Explore sheaf theory's application to Graph Neural Networks, offering a novel perspective on Geometric Deep Learning beyond traditional geometric structures.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Applied Algebraic Topology Network

Analog and Universal Complexity in Robotics and Manifolds

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Explore analog complexity in robotics, comparing digital and analog approaches. Discover surprising properties of analog category and its implications for finite groups and parametrized complexity.
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1 Lesons
1 hour 1 minute
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
Applied Algebraic Topology Network

Katharine Turner - PCA of Persistent Homology Rank Functions with Case Studies

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Explore persistent homology rank functions through PCA, featuring case studies and insights into topological data analysis techniques.
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10 Lesons
57 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Bridging Persistent Homology and Discrete Morse Theory with Applications to Shape Reconstruction

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Explore the connection between persistent homology and discrete Morse theory, unifying key concepts and applying insights to shape reconstruction in computational topology.
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1 Lesons
56 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

On Clustering scRNA-seq Data

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Explore challenges and strategies in clustering single-cell RNA sequencing data, focusing on the k-cluster method's effectiveness for analyzing neuronal datasets in fruit flies.
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1 Lesons
53 minutes
On-Demand
Free-Video