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

## Courses

## Other

Non-academic stuff

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.

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.

Spring 2021:

Topological Data Analysis I (AMAT 583)

Algorithms for Data Science (AMAT 587)

Fall 2020:

Elementary Topology (AMAT 342)

Practical Methods in Topological Data Analysis (AMAT 585)

Spring 2020:

Topological Data Analysis II (AMAT 584)

Master's Seminar (AMAT 680/681/682)

Fall 2019:

Elementary Topology (AMAT 342)

Topological Data Analysis I (AMAT 583)

Spring 2019:

Topics in Topology: Multiparameter persistence (AMAT 840) Course Notes

Honors Calculus II (AMAT/TMAT 119)

Fall 2018:

Honors Calculus I (AMAT/TMAT 118)

Fall 2014 (University of Minnesota):

Applied Linear Algebra (Math 4242),

Topological Data Analysis I (AMAT 583)

Algorithms for Data Science (AMAT 587)

Fall 2020:

Elementary Topology (AMAT 342)

Practical Methods in Topological Data Analysis (AMAT 585)

Spring 2020:

Topological Data Analysis II (AMAT 584)

Master's Seminar (AMAT 680/681/682)

Fall 2019:

Elementary Topology (AMAT 342)

Topological Data Analysis I (AMAT 583)

Spring 2019:

Topics in Topology: Multiparameter persistence (AMAT 840) Course Notes

Honors Calculus II (AMAT/TMAT 119)

Fall 2018:

Honors Calculus I (AMAT/TMAT 118)

Fall 2014 (University of Minnesota):

Applied Linear Algebra (Math 4242),