mlesnick [at] princeton.edu

I'm a mathematician working on topological data analysis (TDA).   I'm an Associate Research Scholar at the Princeton Neuroscience Institute, with a coappointment as a Visitor at the Institute for Advanced Study in the Simons Center for Systems Biology.

Here's my CV.

Research Interests

For some time, my research focused primarily on theoretical foundations of TDA, but in the last three years I've also been getting more involved in the applied and computational side of the subject.   Right now, I'm very interestested in the development of practical new software tools for topological data analysis, 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.

Selected Publications

Universality of the Homotopy Interleaving Distance, w/ Andrew J. Blumberg.   arXiv preprint 1705.01690, 2017.   29 pages.

Persistence Diagrams as Diagrams: A Categorification of the Stability Theorem, w/ Ulrich Bauer.   Submitted; arXiv preprint 1610.10085, 2016.   9 pages.

Algebraic Stability of Zizag Persistence Modules, w/ Magnus Botnan.   Submitted; arXiv preprint arXiv:1604.00655, 2016.   50 pages.

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

Induced Matchings and the Algebraic Stability of Persistence Barcodes, w/ Ulrich Bauer.   SoCG 2014; invited to 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, a friendly introduction to TDA for non-mathematicians.   IAS Letter, Summer 2013.

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

In Fall 2014, I taught Applied Linear Algebra (Math 4242) at the University of Minnesota.

Fun

Music:
Here's some music I made a while ago (in 2006-2009, mostly).   More to come one day.

A Game:
Here are the rules to "Fingernails," a card game I designed in 2010.  It's a very simple SET-like game with a dynamic similar to the children's card game War.  The game is played with a custom deck of 48 round cards. The goal is to decide quickly whether a pair of cards is distance two apart in a certain metric.   You can download a PDF file of the cards here, print them on cardstock (8 color pages), and cut them out.