Thesis advisor: Qile Chen / A (plane) curve is called strange if all of its tangent lines pass through a fixed point, called the strange point. We study the $\mathbb{A}^1$-geometry, and moduli spaces of $\mathbb{A}^1$-curves on the complement of a rational strange plane curve $\Delta$ of degree $p$. On the one hand we observe that $\PP^2\setminus \Delta $ is $\mathbb{A}^1$-connected. On the other hand, these $\mathbb{A}^1$-curves can have large obstructions: therefore $\\mathbb{P}^2\setminus \Delta$ is only inseparably $\mathbb{A}^1$-connected. To understand the strange properties of $\mathbb{A}^1$-curves we study the moduli spaces which parameterize them. In each characteristic, we show the moduli spaces of $\mathbb{A}^1$-curves are connected and classify their irreducible components. The key to the above results are deformation of $\mathbb{A}^1$-curves along certain ``logarithmic" foliations. A direct, and very surprising, consequence of the existence of this foliation is that all $\mathbb{A}^1$-curves are strange. Using the above geometry, we construct for each $p$, new and very explicit examples of supercuspidal families of curves. That is, a fibration with smooth total space but {\it every} fiber is singular with a large number of cusps. / Thesis (PhD) — Boston College, 2021. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Mathematics.

Thesis (doctoral)--Vereinigte Friedrichs-Universität Halle-Wittenberg, 1913. / Cover title. Vita.

Diss.--Breslau (H. Dittrich, A. Koch, and M. Jacobi, respondents). / Title vignette.

Thesis (Ph. D.)--University of Chicago, 1936. / Vita. Lithoprinted. "Private edition, distributed by the University of Chicago libraries, Chicago, Illinois." Includes bibliographical references (p. 30).

Thesis (Ph. D.)--Johns Hopkins University, 1911. / Vita.

Thesis (Ph.D.)--Johns Hopkins university, 1911. / Vita.

No description available.

Thesis (Ph. D.)--John Hopkins University, 1912. / "Reprinted from American journal of mahtematics, vol. XXXVI, no. 1." Biographical.

Thesis (Ph. D.)--University of Chicago, 1915. / Vita. "Reprinted from the Transactions of the American mathematical society, October, 1915." Includes bibliographical references. Also available on the Internet.

Thesis (doctoral)--Albertus-Universität zu Königsberg, 1911. / Vita. Includes bibliographical references.