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Homological Algebra for Persistence Modules

Offered By: Applied Algebraic Topology Network via YouTube

Tags

Homological Algebra Courses Tensor Products Courses Algebraic Topology Courses Persistent Homology Courses Persistence Modules Courses

Course Description

Overview

Explore the rich algebraic theory of persistence modules in this 55-minute lecture by Peter Bubenik. Delve into the world of homological algebra as it applies to persistent homology, where vector spaces are replaced by sequences of vector spaces and linear maps. Learn about key concepts such as tensor products and Hom operations between persistence modules. Discover how these operations produce new persistence modules and examine the challenges in preserving exact sequences when mapping between them. Gain insights into the joint work with Nikola Milicevic that addresses these complexities, offering a deeper understanding of the algebraic structures underlying persistent homology.

Syllabus

Peter Bubenik (10/28/20): Homological Algebra for Persistence Modules


Taught by

Applied Algebraic Topology Network

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