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.
Publications and Preprints
Nicklas Day and Igor Zelenko. (2025). Canonical Frames for Bracket Generating Rank 2 Distributions which are not Goursat. arXiv: 2508.09307 [math.DG]. https://arxiv.org/abs/2508.09307. Accepted to Proceedings of the American Mathematical Society.
Nicklas Day, Boris Doubrov, and Igor Zelenko. (2025). Symplectification of Rank 2 Distributions, Normal Cartan Connections, and Cartan Prolongations. arXiv:2506.09232 [math.DG]. https://arxiv.org/abs/2508.09307. Submitted to Annals mathématiques du Québec.
Preprints in Preparation:
Nicklas Day, Boris Doubrov, and Igor Zelenko. "G_2 and the maximally symmetric rank 3 distribution on R^8 with 6-dimensional square."
Nicklas Day, Igor Zelenko. "An algebraic proof of the existence of strictly normal extremal trajectories."
Brandon Ashley, Nicklas Day, Igor Zelenko. "Rank 2 distributions of sub-submaximal symmetry."
Nicklas Day. "An Invariant Characterizations of Monge Equations."
Nicklas Day, Igor Zelenko. "Unification of Tanaka symbols for rank 2 distributions under iterated Cartan prolongation."
Nicklas Day, Igor Zelenko, Boris Doubrov. "Maximally symmetric rank 3 distributions of non-maximal class."
Slides from Recent Talks
Differential Geometry and its Applications, Brno. Link
Publications During Undergraduate Work
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]