Bernd Sturmfels - Learning Algebraic Varieties from Samples

Explore the intersection of algebraic geometry and data science in this one-hour lecture by Bernd Sturmfels. Delve into methods for determining real algebraic varieties from finite point sets, examining both existing approaches and newly developed techniques. Gain insights into topological and algebraic geometric aspects, including dimension calculation and polynomial definition. Discover practical applications through various datasets, and learn about the implementation of these algorithms in a Julia package. Cover topics such as intrinsic dimension, correlation dimension, dimension diagrams, topological data analysis, tangent spaces, and the connections between algebraic geometry and machine learning. Understand how these concepts apply to real-world examples like cyclooctane datasets and explore their relevance to the broader scientific community.

Introduction
Algebraic varieties
Geometric features
Algebraic geometers
Data
How to sample
Running examples
How to sample point
Intrinsic dimension
Correlation dimension
Dimension diagrams
Topological data analysis
The reach
Tangent spaces
Algebraic geometry
What next
How are we starting
Machine learning
Generalized principle component analysis
Numerical analysis
Cyclooctane
Data sets
Community