My research interests lie broadly in geometry and topology. In particular, I study the construction of curvature-type invariants, Cartan geometry, and Tanaka Theory. I am a student of Dr. Igor Zelenko.
During undergraduate studies, my academic advisor was Dr. Steve Butler. Under Dr. Butler, I studied spectral graph theory, collaborating with peers in the ISMaRT program at Iowa State.
Preprints:
"Rank 2 distributions of sub-submaximal symmetry," Ashley, Brandon; Day, Nicklas; Zelenko, Igor. In preparation.
"An Invariant Characterizations of Monge Equations", Day, Nicklas. In preparation.
 "Symplectification of rank 2 distributions, normal Cartan connections, and Cartan prolongation", Day, Nicklas; Doubrov, Boris; Zelenko, Igor. arXiv:2506.09232. Submitted.
Publications:
Computing Kemeny's constant for a barbell graph (with Jane Breen, Steve Butler, Colt DeArmond, Kate Lorenzen, Haoyang Qian, Jacob Riesen), Electronic Journal of Linear Algebra 35 (2019), 583-598. [doi:10.13001/1081-3810.4095]