Assistant Professor of Mathematics and Statistics, SUNY Albany

mlesnick [at] albany [dot] something

CV
(last updated May 2023).
## Research Interests

I'm a mathematician working primarily on topological
data analysis (TDA). My research focuses on the
theoretical foundations of TDA, and also on the computational and applied aspects of the subject.
A lot of my work is on
multiparameter persistent homology.
## Software

RIVET is practical tool
for the visualization and analysis of two-parameter persistent
homology, designed by Matthew Wright and me, and developed by several people.
## Selected Publications

## Courses

## Other

Non-academic stuff

An introduction to Multiparameter Persistence

w/ Magnus Botnan. Proceedings of the 2020 International Conference on Representations of Algebras, in press. 65 pages.

Stability of 2-Parameter Persistent Homology

w/ Andrew J. Blumberg. Foundations of Computational Mathematics, in press. arXiv:2010.09628, 2020. 44 pages.

Universality of the Homotopy Interleaving Distance

w/ Andrew J. Blumberg. Transactions of the American Mathematical Society, in press. arXiv:1705.01690, 2017. 40 pages.

The Universal ℓ^{p}-Metric on Merge Trees

w/ Robert Cardona, Justin Curry, and Tung Lam. SoCG 2022. 20 pages.

Computing Minimal Presentations and Bigraded Betti Numbers of 2-Parameter Persistent Homology

w/ Matthew Wright. SIAM Journal on Applied Algebra and Geometry 2022. 32 pages.

Computing the Multicover Bifiltration

w/ René Corbet, Michael Kerber, and Georg Osang. SoCG 2021. 17 pages. Extended version invited/accepted to Discrete and Computational Geometry.

ℓ^{p}-Distances on Multiparameter Persistence Modules

w/ Håvard Bakke Bjerkevik. arXiv:2106.13589, 2021. 43 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.

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. Full version invited to the Journal of Computational Geometry. 15 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

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/ Magnus Botnan. Proceedings of the 2020 International Conference on Representations of Algebras, in press. 65 pages.

Stability of 2-Parameter Persistent Homology

w/ Andrew J. Blumberg. Foundations of Computational Mathematics, in press. arXiv:2010.09628, 2020. 44 pages.

Universality of the Homotopy Interleaving Distance

w/ Andrew J. Blumberg. Transactions of the American Mathematical Society, in press. arXiv:1705.01690, 2017. 40 pages.

The Universal ℓ

w/ Robert Cardona, Justin Curry, and Tung Lam. SoCG 2022. 20 pages.

Computing Minimal Presentations and Bigraded Betti Numbers of 2-Parameter Persistent Homology

w/ Matthew Wright. SIAM Journal on Applied Algebra and Geometry 2022. 32 pages.

Computing the Multicover Bifiltration

w/ René Corbet, Michael Kerber, and Georg Osang. SoCG 2021. 17 pages. Extended version invited/accepted to Discrete and Computational Geometry.

ℓ

w/ Håvard Bakke Bjerkevik. arXiv:2106.13589, 2021. 43 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.

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. Full version invited to the Journal of Computational Geometry. 15 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

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 2023:

Topics in Topology: Multiparameter Persistent Homology (AMAT 840)

Topological Data Analysis II (AMAT 584)

Fall 2022:

Topics in Topology: Multiparameter Persistent Homology (AMAT 840)

Topological Data Analysis I (AMAT 583)

Spring 2022:

Algorithms for Data Science (AMAT 587)

Practical Methods in Topological Data Analysis (AMAT 585)

Fall 2021:

Elementary Topology (AMAT 342)

Topological Data Analysis II (AMAT 584)

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),

Topics in Topology: Multiparameter Persistent Homology (AMAT 840)

Topological Data Analysis II (AMAT 584)

Fall 2022:

Topics in Topology: Multiparameter Persistent Homology (AMAT 840)

Topological Data Analysis I (AMAT 583)

Spring 2022:

Algorithms for Data Science (AMAT 587)

Practical Methods in Topological Data Analysis (AMAT 585)

Fall 2021:

Elementary Topology (AMAT 342)

Topological Data Analysis II (AMAT 584)

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),