Algebraic Topology and Algebraic Geometry for Data Science

Algebraic geometry is the study of the zero sets to general systems of polynomials called varieties; it turns out that varieties encode important real data phenomena.  An important example is phylogenetic trees, which are fundamental data structures in biology and with which I have worked extensively.  They are also interesting data objects in their own right; there is currently an active interest in studying characteristics of varieties using computational and machine learning methods, which I will discuss.  Algebraic topology studies properties of spaces that are preserved under smooth transformations.  This is a field that is adaptable to real data because the presence of noise and noisy perturbations in real world data can be seen as such a smooth transformation.  These two fields of pure mathematics together provide a powerful toolkit to understanding, modeling, and analyzing data, data generating processes, statistical models, and machine learning methods.  In this talk, I will give an overview of some examples from my work on various algebraic geometric and algebraic topological approaches that develop theory for data analytic methodology as well as real data analyses using techniques based on these fields of pure mathematics.

Bio: Anthea Monod is a mathematical data scientist who works at the interface of pure mathematics, statistics, and machine learning.  She is an Assistant Professor at the Department of Mathematics at Imperial College London, where she currently leads a large group of researchers including postdocs, PhD students, MSc students, visiting scholars, and undergraduate research assistants.  She is also an Emmy Noether Fellow of the London Mathematical Society.  She completed her PhD at EPFL and, prior to her current permanent position at Imperial, she held postdoctoral and visiting researcher positions at the Technion, Duke University, and Columbia University.