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Persistent Topological Laplacians

Offered By: Applied Algebraic Topology Network via YouTube

Tags

Topological Data Analysis Courses High-Dimensional Data Analysis Courses

Course Description

Overview

Explore the cutting-edge developments in topological data analysis (TDA) through this comprehensive lecture on persistent topological Laplacians (PTLs). Delve into the limitations of persistent homology (PH) and discover how PTLs address these challenges. Learn about various types of PTLs, including persistent Laplacians, persistent path Laplacians, persistent sheaf Laplacians, persistent hypergraph Laplacians, persistent hyperdigraph Laplacians, and evolutionary de Rham-Hodge theory. Understand how these advanced tools, when combined with artificial intelligence algorithms, have been applied to uncover the mechanisms of SARS-CoV-2 evolution and accurately forecast emerging dominant variants. Gain insights into the exponential growth of TDA's impact in sciences and engineering, and its ability to handle complex, high-dimensional, nonlinear, and multiscale data.

Syllabus

Guo-Wei Wei (4/28/2023): Persistent Topological Laplacians


Taught by

Applied Algebraic Topology Network

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