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Vietoris-Rips Thickenings - Problems for Birds and Frogs

Offered By: Applied Algebraic Topology Network via YouTube

Tags

Vietoris-Rips Complexes Courses Measure Theory Courses Algebraic Topology Courses Geometric Group Theory Courses Homotopy Theory Courses Metric Geometry Courses

Course Description

Overview

Explore open problems related to Vietoris-Rips complexes in this comprehensive lecture by Henry Adams. Delve into the fascinating world of applied algebraic topology, where mathematicians are categorized as "birds" who connect broad theories, and "frogs" who solve specific problems. Discover attractive challenges for both types of mathematicians, including the homotopy types of Vietoris-Rips complexes for various geometric objects and spaces. Uncover emerging connections between Vietoris-Rips complexes and diverse areas of pure mathematics, such as metric geometry, quantitative topology, measure theory, topological combinatorics, geometric group theory, and geometric topology. Gain insights into the mathematical properties of Vietoris-Rips complexes and their applications in approximating dataset shapes. Access accompanying slides for a visual understanding of the concepts presented in this engaging 1-hour 18-minute talk from the Applied Algebraic Topology Network.

Syllabus

Henry Adams (3/12/21): Vietoris-Rips thickenings: Problems for birds and frogs


Taught by

Applied Algebraic Topology Network

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