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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, Logic and Set Theory, and Calculus.

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

My other interests include: short stories, theatre, making a great defensive play in pickup basketball and immediately getting my shot blocked on the other end of the court; playing soccer until my ankles spontaneously combust; and walking very, very long distances at a calm and steady pace.

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

(2021). Extremal {p,q}-Animals. arXiv preprint.

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(2021). 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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(2019). Collapsibility of Random Clique Complexes. arXiv preprint.

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

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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

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.

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

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