Computational topology and genomics research

I am interested in topological data analysis (TDA) and more broadly the use of topology and geometry to analyze data. I work on
Testing to distinguish measures on metric spaces
joint with Prithwish Bhaumik and Stephen G. Walker.
Topological data analysis for genomics and evolution
joint with Raul Rabadan. Cambridge University Press, to appear 2018.
In preparation (under contract)
Geometry and topology of genomic data
joint with Raul Rabadan.
Chapter 66 in Handbook of Discrete and Computational Geometry (Third edition). J.E. Goodman, J. O'Rourke, and C.D. Toth, editors.
published version
Universality of the homotopy interleaving distance
joint with Mike Lesnick.
Spatiotemporal genomic architecture informs precision oncology in glioblastoma
joint with Jin-Ku Lee, Jiguang Wang, Jason K Sa, Erik Ladewig, Hae-Ock Lee, In-Hee Lee, Hyun Ju Kang, Daniel S Rosenbloom, Pablo G Camara, Zhaoqi Liu, Patrick Van Nieuwenhuizen, Sang Won Jung, Seung Won Choi, Junhyung Kim, Andrew Chen, Kyu-Tae Kim, Sang Shin, Yun Jee Seo, Jin-Mi Oh, Yong Jae Shin, Chul- Kee Park, Doo-Sik Kong, Ho Jun Seol, Jung-Il Lee, Antonio Iavarone, Woong-Yang Park, Raul Rabadan, Do-Hyun Nam.
Nature Genetics 49 (2017), 594–599.
published version
A polynomial-time relaxation of the Gromov-Hausdorff distance
joint with Soledad Villar, Afonso Bandeira, and Rachel Ward.
Clonal evolution of glioblastoma under therapy
joint with Jiguang Wang, Emanuela Cazzato, Erik Ladewig, Veronique Frattini, Daniel I. S. Rosenbloom, Sakellarios Zairis, Francesco Abate, Zhaoqi Liu, Oliver Elliott, Yong-Jae Shin, Jin-Ku Lee, In-Hee Lee, Woong-Yang Park, Marica Eoli, Anna Lasorella, Do-Hyun Nam, Gaetano Finocchiaro, Antonio Iavarone, and Raul Rabadan.
Nature Genetics 48 (2016), 768-776.
published version
Genomic data analysis in tree spaces
joint with Sakellarios Zairis, Hossein Khiabanian, and Raul Rabadan.
Moduli spaces of phylogenetic trees describing tumor evolutionary patterns.
joint with Sakellarios Zairis, Hossein Khiabanian, and Raul Rabadan.
Springer Lecture Notes in Computer Science 8609 (2014).
published version
Persistent homology for metric measure spaces, and robust statistics for hypothesis testing and confidence intervals
joint with Itamar Gal, Mike Mandell, and Matt Pancia.
Foundations of Computational Mathematics 14 (2014), 745-789.
published version
Quantitative homotopy theory in topological data analysis
joint with Mike Mandell.
Foundations of Computational Mathematics 13 (2013), 885-911.
published version