Greg Malen

Visiting Assistant Professor

Union College

About Me

I am a Visiting Assistant Professor of Mathematics at Union College. My research interests include topological and geometric data analysis, topological combinatorics, and combinatorial and stochastic topology. At Union I teach courses in Discrete Math, Probability, Geometry, Logic and Set Theory, and Calculus.

In addition to my teaching and research, I regularly supervise student research projects and independent studies in both pure and applied topics. I also run Union’s incredibly fun Putnam team, and I serve as the Faculty Advisor for the Women’s Soccer team.

My other interests include: short stories; theatre and the performing arts; chess and old school card games; making a great defensive play in pickup basketball and immediately getting my shot blocked on the other end of the court; and playing soccer until my ankles spontaneously combust.

Interests

Random Cell Complexes
Graph Theory
Topological Data Analysis
Polyforms

Education

PhD in Mathematics, 2016
The Ohio State University
BA in Mathematics and in Theatre, 2007
Wesleyan University

Publications and Preprints

Greg Malen, Fedor Manin, Érika Roldán (2022). High-dimensional holeyominoes. The Electronic Journal of Combinatorics.

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Greg Malen, Rosemberg Toalá-Enríquez, Érika Roldán (2021). Extremal {p,q}-Animals. arXiv preprint.

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Greg Malen, Érika Roldán (2020). Polyiamonds attaining extremal topological properties, part 2. Geombinatorics.

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Greg Malen, Érika Roldán (2020). Polyiamonds attaining extremal topological properties, part I. Geombinatorics.

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Michael J. Catanzaro, Justin Curry, Brittany Terese Fasy, Jānis Lazovskis, Greg Malen, Hans Riess, Bei Wang, Matthew Zabka (2020). Moduli spaces of morse functions for persistence. Journal of Applied and Computational Topology.

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Greg Malen, Érika Berenice Roldán-Roa (2020). Extremal topological and geometric problems for polyominoes. The Electronic Journal of Combinatorics.

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Greg Malen (2019). Collapsibility of Random Clique Complexes. arXiv preprint.

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Greg Malen (2018). Homomorphism complexes and $k$-cores. Discrete Mathematics.

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Greg Malen (2016). The topology of random flag and graph homomorphism complexes. PhD Thesis.

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Greg Malen (2015). Measurable colorings of $S^2_r$. Geombinatorics.

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Selected Talks

The Topology and Structure of Crystallized Polyforms. SUNY at Albany Algebra/Topology Seminar, October 2019.

Dense Random Clique Complexes. JMM Special Session on Topological Data Analysis, January 2018.

k-Collapsibility of Random Clique Complexes. IMA Applied Algebraic Topology Research Network, February 2017.

Teaching

At Union:

Topics in Discrete Mathematics (Fall 2021, Fall 2022), Intro to Logic and Set Theory (Winter 2022) Probability (Winter 2021, Spring 2021, Winter 2022), Geometry (Spring 2021), Accelerated Single Variable Calculus (Fall 2020, Winter 2021, Fall 2022), Single Variable Calculus (Spring 2022).

At Duke:

Probability (Spring 2017, 2018, 2019; Fall 2017, 2019), Advanced Introduction to Probability (Spring 2020), Combinatorics (Fall 2018), Topological Data Analysis (Spring 2018), Topics in Applied Topology (Spring 2020).

Extremal Polyforms

You can explore extremal hyperbolic polyforms via our applet at https://www.erikaroldan.net/extremal-p-q-animals. A crystallized polyform is one with the minimal number of tiles necessary to support the number of bounded holes in the structure.