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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 and the Math Club on campus. I am also on the steering committee for the annual Hudson River Undergraduate Math Conference (HRUMC); 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

(2023). Extremal {p,q}-Animals. Annals of Combinatorics.

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

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(2022). High-dimensional holeyominoes. The Electronic Journal of Combinatorics.

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(2020). Polyiamonds attaining extremal topological properties, part 2. Geombinatorics.

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(2020). Polyiamonds attaining extremal topological properties, part I. Geombinatorics.

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(2020). Moduli spaces of morse functions for persistence. Journal of Applied and Computational Topology.

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(2020). Extremal topological and geometric problems for polyominoes. The Electronic Journal of Combinatorics.

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

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(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

Courses for Fall 2023 (more info available in September):

MA 113: Calc 2. M 9:05-10:00am, Tu/Th 9:40-11:00am in Annex 216

MA 215: Intro to Proof. M 1:25-2:20pm, Tu/Th 2:10-3:30pm in Bolton 100

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.

$$T_{315}\ast Spir_8$$ 1033 tiles and 315 holes

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