**Research Overview**

My research currently resides in areas of geometric number theory, arrangement theory, and sports analytics.

**Scholarly Works**

- Powers of Two as Sums of Two Balancing Numbers (with B. Dearden, J. Iiams, and J. Peterson). In F. Hoffman, S. Holliday, Z. Rosen, F. Shahrokhi, and J. Wierman (Ed.),
*Combinatorics, Graph Theory and Computing*, Springer Proc. Math. Stat., vol. 448, pp. 383-392, 2024. - Good Things Come in Threes: A Ternary Tree for Triangular Triples,
*Math. Mag.*, vol. 96(1), pp. 1-6, 2023. doi: 10.1080/0025570X.2023.2177060. - Ratio Balancing Numbers (with B. Dearden, J. Iiams, and J. Metzger). In F. Hoffman (Ed.),
*Combinatorics, Graph Theory and Computing*, Springer Proc. Math. Stat., vol. 388, pp. 1-12, 2022. - Jump Sizes for Polygonal Balancing Numbers (with B. Dearden and J. Iiams),
*Australas. J. Combin.*, vol. 83(3), pp. 337-347, 2022. - Polygonal Balancing Numbers I (with B. Dearden and J. Iiams),
*Integers*, 22(A54), 2022. - Classes of Gap Balancing Numbers (with B. Dearden and J. Iiams),
*Rocky Mountain J. Math.*, vol. 51(2), pp. 399-411, 2021. - Risk it all or play it safe? Exploring probability through Farkle. In M. Capaldi (Ed.),
*Teaching Mathematics through Games*, MAA Press Classroom Resource Materials series, vol. 65, pp. 57-62, 2021. - Counting Families of Generalized Balancing Numbers (with B. Dearden and J. Iiams),
*Australas. J. Combin.*, vol. 77(3), pp. 318-325, 2020. - Almost Gap Balancing Numbers (with B. Dearden and J. Iiams),
*Integers*, 18(A79), 2018. - Induced and Complete Multinets. In D. Ibadula and W. Veys (Ed.),
*Configuration Spaces: Geometry, Topology, and Representation Theory*, Springer INdAM Ser., vol. 14, pp. 213-231, 2016. - A Mixed-Methods Study on Pre-licensure Nursing Students Changing Answers on Multiple Choice Examinations (with T. George and M. Muller),
*Journal of Nursing Education,*2016 Apr 1; 55(4):220-3. doi: 10.3928/01484834-20160316-07. - Multinets in P^2 (with S. Yuzvinsky),
*Bridging Algebra, Geometry, and Topology*, Springer Proceedings in Mathematics and Statistics, vol. 96, 2014.

**Descriptions of Research Interests**

**Arrangement Theory**

Arrangement theory is a branch of discrete geometry which studies collections of geometric objects and their properties. My research lies in the area of complex hyperplane arrangements, finite collections of hyperplanes in the complex projective plane. More specifically, I study configurations of points and lines which satisfy certain intersection properties called

*nets*and

*multinets*. These configurations play an important role in the study of resonance varieties of complex hyperplane arrangement complements.

**Geometric Number Theory**

Geometric constructions give rise to many interesting sequences. More specifically, two colleagues and I have been studying sequences related to when the sum of triangular numbers is again a triangular number.

**Sports Analytics**

Sports analytics has been also an area of interest for me. Some colleagues at the University of North Dakota and I are investigating sports data to better understand athletic events.