mlesnick [at] albany.edu

I'm a mathematician working on topological data analysis (TDA).   As of September 2018, I'm an Assistant Professor in the Department of Mathematics at SUNY Albany.

Here's my CV (last updated April 2018).

Research Interests

For some time, my research focused primarily on theoretical foundations of TDA, but recently I've also been getting more involved in the applied and computational side of the subject.   Right now, I'm 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.

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.   Recently, we finished some substantial improvements to RIVET, and finally did a proper release of the software in the summer of 2018.   Among other things, the new version of RIVET features a fast (cubic time) algorithm for computing a minimal presentation of a 2-parameter persistent homology module.   A paper on this is in the works.

Selected Publications

Persistent Homology for Virtual Screening
w/ Bryn Keller (first author), Ted Wilke.   Submitted, 2018.   29 pages.

Quantifying Genetic Innovation: Mathematical Foundations for the Topological Study of Reticulate Evolution
w/ Raul Rabadán, Daniel I.S. Rosenbloom.   Submitted; arXiv:1804.01398, 2018.   44 pages.

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

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

Algebraic Stability of Zizag Persistence Modules
w/ Magnus Botnan.   Accepted to Algebraic and Geometric Topology; arXiv:1604.00655, 2016.   50 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 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

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

Other

Music:
Here's some music I made a while ago (in 2006-2009, mostly); more to come one day.   And here are five pieces of piano music my wife Minhee composed in 2016.

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.