Topological Data Analysis for Genomics and Evolution

Raul Rabadan is a Professor at Columbia University, New York. He is Director of the Program for Mathematical Genomics at Columbia University, New York, and the NCI Physics and Oncology Center for Topology of Cancer Evolution and Heterogeneity. Dr Rabadan received his Ph.D. in Theoretical Physics in 2001 and went on to conduct research at the European Laboratory for Particle Physics (CERN) in Switzerland, and at the Institute for Advanced Study (IAS), Princeton, New Jersey. At Columbia University, he leads a highly interdisciplinary laboratory with researchers from the fields of mathematics, physics, computer science, engineering, and medicine, with the common goal of solving biomedical problems through quantitative computational models. Andrew J. Blumberg is a Professor in the Department of Mathematics at the University of Texas, Austin. He completed his Ph.D. at the University of Chicago under the supervision of Peter May and Michael Mandell, and was later a National Science Foundation postdoctoral fellow at Stanford University, California. He also spent a year as a member at the Institute for Advanced Study (IAS), Princeton, New Jersey. His pure mathematics research focuses primarily on homotopy theory and algebraic topology and his applied research focuses on the development of topological and geometric techniques for studying genomic data.

'The time is right to bring new approaches to the analysis of biological data. Topological data analysis reveals the structure of data. This book shows how algebraic topology opens new doors, presenting ideas and directions that make testable predictions and explore life processes.' Arnold J. Levine, Institute for Advanced Study, New Jersey

• Introduction; Part I. Topological Data Analysis: 1. Basic notions of algebraic topology; 2. Topological data analysis; 3. Statistics and topological inference; 4. Manifold learning and metric geometry; Part II. Biological Applications: 5. Evolution, trees, and beyond; 6. Cancer genomics; 7. Single cell expression data; 8. Three dimensional structure of DNA; 9. Topological data analysis beyond genomics; 10. Conclusions.