Greg Malen

Assistant Professor

Skidmore College

About Me

I am an Assistant Professor of Mathematics at Skidmore College. My research interests include topological and geometric data analysis, topological combinatorics, and combinatorial and stochastic topology.

In addition to my teaching and research, I regularly supervise student research projects and independent studies in both pure and applied topics. I supervise the Putnam exam and other regional math competitions that students can compete in, and I am the Faculty Advisor for Skidmore’s Pi Mu Epsilon chapter. I am also on the steering committee for the annual Hudson River Undergraduate Math Conference (HRUMC). This year’s conference will be held at Vassar College on Saturday April 25th; for more info see https://sites.google.com/view/hrumc.

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

Jason D’Amico, Greg Malen, Ellen Gasparovic, Mushan Zhong (2025). A medial-axix-based measure of district compactness. The PUMP Journal of Undergraduate Research.

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Greg Malen, Rosemberg Toalá-Enríquez, Érika Roldán (2023). Extremal {p,q}-Animals. Annals of Combinatorics.

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Greg Malen (2023). Collapsibility of Random Clique Complexes. To appear in Discrete Mathematics.

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

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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 (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_{r}^{2}

. Geombinatorics.

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Selected Talks

An Expansion Regime for Random Clique Complexes. AMS 2024 Fall Eastern Sectional Meeting at SUNY at Albany, October 2024

Graph Homomorphisms and Topological Bounds on Chromatic Number. Union College Math Department Student Seminar, May 2024.

Extremal Polyforms and Hyperbolic Animals. Carnegie Mellon University Algorithms, Combinatorics and Optimization Seminar, November 2023.

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

I’m currently on sabbatical for Spring 2026. My scheduled courses for Fall 2026 are:

MA 225H: Honors: Problem Solving. W 4:00-5:20pm

MA 313: Intro to Topology. Tu/Th 11:10am-12:30pm

SSP: Stories Covered in Chalk. M 1:25-2:20pm, Tu/Th 2:10-3:30pm

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.