Research Interests

I am currently an Assistant Professor of Data Analytics in the Department of Mathematics and Statistics at Washington State University. Previously, I was a postdoctoral associate at MIT (CSAIL) in the Geometric Data Processing Group, working under Justin Solomon and associated with the Metric Geometry and Gerrymandering Group at MIT and Tufts, working with Moon Duchin and Justin Solomon on the mathematics of redistricting. I earned my Ph.D. in mathematics at Dartmouth College under the supervision of Dan Rockmore in 2018. My research interests tend towards applications of algebraic and combinatorial methods in data analysis.

### Croasdale Award

In 2018, I won the Hannah Croasdale Award, which is a college-wide award awarded annually to the graduating PhD recipient who best exemplifies the qualities of a scholar. An article from the graduate school focused on my research experiences can be found: here.

### Research Articles

#### Accepted Papers

1. Medial Axis Isoperimetric Profiles, with P. Zhang and J. Solomon, SGP, (to appear 2020).
2. A Computational Approach to Measuring Vote Elasticity and Competitiveness, with M. Duchin and J. Solomon, Statistics and Public Policy, (to appear 2020).
3. Mathematics of Nested Districts: The Case of Alaska, with S. Caldera, M. Duchin, S. Gutenkust, and C. Nix, Statistics and Public Policy, (to appear 2020).
4. On the Spectrum of Finite Rooted Homogeneous Trees, with D. Rockmore, Linear Algebra and Applications, 598, 165-185, (2020).
5. Aftermath: The Ensemble Approach to Political Redistricting, with J. Clelland and M. Duchin, MAA Math Horizons, 28(1), 34-35, (2020).
6. Total Variation Isoperimetric Profiles, with H. Lavenant, Z. Schutzman, and J. Solomon, SIAM J. Appl. Algebra Geometry, 3(4), 585-613, (2019).
7. Spectral Clustering Methods for Multiplex Networks, with S. Pauls, Physica A, 121949, (2019).
8. Redistricting Reform in Virginia: Districting Criteria in Context, with M. Duchin, Virginia Policy Review, 12(2), 120-146, (2019).
9. A new framework for dynamical models on multiplex networks, with S. Pauls, Journal of Complex Networks, 6(3), 353-381, (2018).
10. Multiplex Dynamics on the World Trade Web, Proc. 6th International Conference on Complex Networks and Applications, Studies in Computational Intelligence, Springer, 1111-1123, (2018).
11. Cyclic Groups with the same Hodge Series, with P. Doyle, Revista de la UMA, 59(2), 241-254, (2018).
12. Random Walk Null Models for Time Series Data, with K. Moore, Entropy, 19(11):615, (2017).
13. Enumerating Tilings of Rectangles by Squares, Journal of Combinatorics, 6(3), 339-351, (2015).
14. Pulsated Fibonacci Sequences, with K. Atanassov and A. Shannon, Fibonacci Quarterly (Conference Proceedings), 52(5), 22-27 (2014).
15. Enumerating Distinct Chessboard Tilings , Fibonacci Quarterly (Conference Proceedings), 52(5), 102-116, (2014).
16. Seating Rearrangements on Arbitrary Graphs, Involve, 7(6), 787-805, (2014).
17. Empirical Analysis of Space-Filling Curves for Scientific Computing Applications, with A. Kalyanaraman, Proceedings of the 42nd International Conference of Parallel Processing, 170-179, (2013).
18. Counting Rearrangements on Generalized Wheel Graphs, Fibonacci Quarterly, 51(3), 259-273, (2013).
19. #### Preprints

20. Partisan Dislocation: A Precinct-Level Measure of Representation and Gerrymandering, with N. Eubank and J. Rodden, submitted, (2020).
21. Complexity and Geometry of Sampling Connected Graph Partitions, with L. Najt and J. Solomon, arXiv:1908.08881, (2019).
22. ReCombination: A family of Markov chains for redistricting, with M. Duchin and J. Solomon, arXiv:1911.05725, (2019).
23. Fourier transforms on $$SL_2(\mathbb{Z}/p^n\mathbb{Z})$$ and related numerical experiments, with B. Breen, J. Linehan, and D. Rockmore, arxiv: 1710.02687, (2017).
24. A Random Dot Product Model for Weighted Networks, with D. Rockmore, arXiv:1611.02530, (2016).
25. #### Technical Reports

26. Comparison of Districting Plans for the Virginia House of Delegates, with M. Duchin and J. Solomon, MGGG Technical Report, (2019).
27. Amicus Brief of Mathematicians, Law Professors, and Students, M. Duchin and G. Charles et al., Rucho v. Common Cause, (2019).
28. Study of Reform Proposals for Chicago City Council, with M. Duchin et al., MGGG Technical Report, (2019).
29. An Application of the Permanent-Determinant Method: Computing the Z-index of Arbitrary Trees, WSU Technical Report Series #2013-2, (2013).

### Other Writing

1. Introduction to Discrete MCMC for Redistricting (with Scrabble) (2019).
• A friendly and interactive introduction to discrete MCMC methods, concluding with applications to political redistricting. Many of the motivating examples are explained with Scrabble tiles. Accompanying Sage-interact widgets embedded on a webpage here and also on GitHub.
2. Building Ensembles of Graph Partitions (2019)
• This is a guide to GerryChain that walks through the engineering challenges inherent in generating ensembles of districting plans. Contains numerous examples and code snippets. Frequently updated.
3. Geospatial Data Preparation for GerryChain (2019)
• Beginning to end description of the data preparation process for building an annotated dual graph for GerryChain. Frequently updated.
4. Applied Mathematics and Network Science (2018).
• This is a short piece describing my personal philosophy of applied mathematics and addressing the differences between graphs and networks.
5. The Written Qual Book (with D. Freund) (2017).
• This is a 274 page book containing solutions to all of the written qualifying exam problems that were given in the Dartmouth Math Department from 2012-2017. In addition to the solutions, we included 20 pages of expository material on how to survive graduate school and many helpful appendices. There are also 60 pages of notes, commentary, and context to supplement the formal solutions.