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#Persistence Modules

Showing: 18 courses
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
On-Demand
Free-Video
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
On-Demand
Free-Video
Applied Algebraic Topology Network

Detecting Bifurcations in Dynamical Systems with Zigzag Persistent Homology

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Explore zigzag persistent homology for efficient detection of bifurcations in dynamical systems, reducing computational costs and capturing topological changes in a single persistence diagram.
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11 Lesons
24 minutes
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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
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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

Limit Theorems in Topological Data Analysis

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Explore limit theorems in topological data analysis, focusing on barcodes, persistence modules, and random persistence modules. Learn about convergence proofs and expectations for uniform distributions on compact submanifolds.
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15 Lesons
58 minutes
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

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
On-Demand
Free-Video
Applied Algebraic Topology Network

Vanessa Robins - The Extended Persistent Homology Transform for Manifolds with Boundary

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Explore extended persistent homology transform for shape analysis, offering finite distances between shapes with different Betti numbers and applications in shape clustering.
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9 Lesons
59 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Saecular Persistence

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Explore saecular persistence, a method to decompose persistence modules with non-field coefficients. Learn about applications in topology, generalized persistence diagrams, and scientific data analysis.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Applied Algebraic Topology Network

Homological Algebra for Persistence Modules

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Introduction to persistence modules in algebraic topology, exploring tensor products, Hom operations, and their role in homological algebra. Insights into preserving exact sequences and advanced concepts.
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1 Lesons
55 minutes
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Free-Video
Applied Algebraic Topology Network

Extracting Persistence Features with Hierarchical Stabilisation

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Explore hierarchical stabilisation for extracting stable invariants from persistence modules, focusing on the stable rank and its applications in data analysis and classification tasks.
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1 Lesons
43 minutes
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Free-Video
Applied Algebraic Topology Network

On the Algebraic Geometry of Spaces of Persistence Modules

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Explore algebraic geometry's application to persistence modules in topological data analysis, offering insights into data structure and shape analysis.
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1 Lesons
46 minutes
On-Demand
Free-Video
BIMSA

On the Hofer-Zehnder Conjecture - Periodic Points of Hamiltonian Diffeomorphisms

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Explore Hofer-Zehnder conjecture on periodic points of Hamiltonian diffeomorphisms, examining recent progress using persistence modules, barcodes, and Floer cohomology power operations.
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1 Lesons
54 minutes
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Free-Video
Applied Algebraic Topology Network

Generalized Persistence Algorithm for Decomposing Multi-Parameter Persistence Modules

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Explore a generalized persistence algorithm for decomposing multi-parameter persistence modules, enhancing topological data analysis with improved computational efficiency and structural insights.
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10 Lesons
54 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Parallel Decomposition of Persistence Modules Through Interval Bases

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Exploring parallel decomposition of persistence modules using interval bases, with applications in Topological Data Analysis and connections to the Hodge Laplacian.
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13 Lesons
51 minutes
On-Demand
Free-Video
Applied Algebraic Topology Network

Harder-Narasimhan Filtrations of Persistence Modules

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Explore Harder-Narasimhan types in quiver representations, examining their applications and limitations in persistence modules across various contexts in algebraic topology.
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1 Lesons
50 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