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UWSpace will be migrating to a new version of its software from July 29th to August 1st. UWSpace will be offline for all UW community members during this time.
The objective of this thesis is to bound the number of points a $U_{2,\ell+2}$- and $M(K_{k+1})$-minor-free matroid has. We first prove that a sufficiently large matroid will contain a structure called a tower. We then use towers to find a complete minor in a matroid with no $U_{2,\ell+2}$-minor.