Michael Lesnick

Mike_Four_Corners

Assistant Professor of Mathematics, SUNY Albany
mlesnick [at] albany [dot] something
CV (last updated January 2021).

Research Interests

I'm a mathematician working primarily on topological data analysis (TDA).   For some time, my research focused on theoretical foundations of TDA, but in the last few years, I've also been getting more involved in the applied and computational side of the subject.   In particular, I'm interested in the development of new practical software tools for TDA, and in applications to biology.   Much of my work on both the theoretical and applied sides concerns multidimensional persistent homology and the algebraic aspects of TDA.

Software

Matthew Wright and I have designed and (in collaboration with several others) developed a practical tool for the visualization and analysis of two-parameter persistent homology, called RIVET.

Selected Publications

Stability of 2-Parameter Persistent Homology
w/ Andrew J. Blumberg.   arXiv:2010.09628, 2020.   44 pages.

Persistence Diagrams as Diagrams: A Categorification of the Stability Theorem
w/ Ulrich Bauer.   Proceedings of the 2018 Abel Symposium (published in 2020).   30 pages.

Quantifying Genetic Innovation: Mathematical Foundations for the Topological Study of Reticulate Evolution
w/ Raul Rabadán, Daniel I.S. Rosenbloom.   SIAM Journal of Applied Algebra and Geometry, 2020.   44 pages.

Computing Minimal Presentations and Bigraded Betti Numbers of 2-Parameter Persistent Homology
w/ Matthew Wright.   Submitted, 2019.   29 pages.

Feasibility of topological data analysis for event-related fMRI
w/ Cameron T. Ellis (first author), Gregory Henselman-Petrusek, Bryn Keller, Jonathan D. Cohen.   Network Neuroscience, 2019.   24 pages.

Exact computation of the matching distance on 2-parameter persistence modules
w/ Michael Kerber, Steve Oudot.   SoCG 2019. Invited/Accepted to the Journal of Computational Geometry.   15 pages.

Universality of the Homotopy Interleaving Distance
w/ Andrew J. Blumberg.   In revision; arXiv:1705.01690, 2017.   29 pages.

Algebraic Stability of Zizag Persistence Modules
w/ Magnus Botnan.   Algebraic & Geometric Topology, 2018.   72 pages.

Interactive Visualization of 2-D Persistence Modules
w/ Matthew Wright.   Submitted; arXiv:1512.00180, 2015.   75 pages.

Induced Matchings and the Algebraic Stability of Persistence Barcodes
w/ Ulrich Bauer.   SoCG 2014; invited to the Journal of Computational Geometry, 2015.   30 pages.

The Theory of the Interleaving Distance on Multidimensional Persistence Modules
Journal of Foundations of Computational Mathematics, 2015.   36 pages.

Studying the Shape of Data Using Topology
IAS Letter, Summer 2013.   A friendly introduction to TDA for non-mathematicians.

Multidimensional Interleavings and Applications to Topological Inference
Ph.D. thesis, 2012.   Winner, Gene Golub Dissertation Award.     Note: Chapters 2 and 3 of this thesis are, respectively, largely subsumed by the above 2015 FoCM paper and 2017 preprint with Andrew Blumberg.  

Courses

Other

Non-academic stuff