Research-How to do science with topological data analysis

Research

Colloquium

How to do science with topological data analysis

Speaker: Andrew Blumberg (University of Texas at Austin)
Time: Nov 6, 2020, 11:00-12:00
Location: Zoom (ID 642 0299 8817)

Abstract

Topological data analysis (TDA) is a methodology for using tools from algebraic topology to obtain information about the “shape” of data sets. The most popular TDA algorithms provide multiscale invariants that capture subtle geometric properties in data. Although it seems evident that such methods should be of tremendous scientific value, there are many technical and conceptual challenges associated to efforts to use TDA in applications. This talk will provide a gentle overview of ideas from TDA as well as an approach to applying these methods for scientific inference, motivated by applications from genomics.

About the speaker

Andrew Blumberg is a Professor of Mathematics at the University of Texas, Austin and a visiting Professor in the Department of Mathematics and Computer Science at Columbia University and the Irving Institute for Cancer Dynamics. Prior to arriving in Austin, he was an NSF postdoctoral fellow from 2005 to 2009 at Stanford, with a year’s stint as a member at the Institute for Advanced Study in 2007–2008. Prof. Blumberg received his Ph.D. in 2005 from the University of Chicago.

Prof. Blumberg has broad research interests in mathematics and computer science. His research includes work in algebraic topology, topological data analysis, and computer security and privacy, with publications in distinguished research journals such as Invent. Math., Acta Math., and Mem. Amer. Math. Soc. He is particularly interested in the applications of geometry and topology to the analysis of genomic data and has co-authored the book “Topological Data Analysis for Genomics and Evolution: Topology in Biology” recently published by the Cambridge University Press.

Prof. Blumberg is an editor for the Journal of Topology, an associate editor for Advances in Mathematics, and an editor for the Journal of Applied and Computational Topology. He is a member of the Center for Topology of Cancer Evolution and Heterogeneity based at Columbia University. He is also part of the Pepper project at New York University on verifiable outsourced computing.