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.

- Random Cell Complexes
- Graph Theory
- Topological Data Analysis
- Polyforms

PhD in Mathematics, 2016

The Ohio State University

BA in Mathematics and in Theatre, 2007

Wesleyan University

(2021).
(2021).

Polyiamonds attaining extremal topological properties, part 2.
Geombinatorics.

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

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

(2020).
(2019).
(2018).
(2016).
(2015).
*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.

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

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).

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.