Greg Malen

Visiting Assistant Professor

Union College

About Me

I am a Visiting Assistant Professor of Mathematics at Union College. I completed my PhD at The Ohio State University in 2016 under the advisement of Matthew Kahle. I then spent a semester as a research fellow at the Institute for Experimental and Computational Research in Mathematics (ICERM) and three years as a postdoc at Duke University before arriving at Union.

My research interests include topological combinatorics, combinatorial and stochastic topology, topological and geometric data analysis, and combining the names of primary areas of research to describe more specific areas of research.

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

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Greg Malen, Fedor Manin, Érika Roldán (2021). High-dimensional holeyominoes. 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 Math.

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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:

Probability (Winter 2021, Spring 2021), Geometry (Spring 2021), Accelerated Single Variable Calculus (Fall 2020, Winter 2021).

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.