An Erdos-Turan Inequality For Compact Simply-Connected Semisimple Lie Groups

The classical Erd{\" o}s-Turan Inequality bounds how far a sequence of points in the circle is from being equidistributed in terms of its exponential moments. We prove an analogous inequality for all compact simply-connected semisimple Lie groups, bounding how far a sequence is from being equidistributed in the conjugacy classes of the group in terms of the moments of irreducible characters.Comment: 21 page

The importance of vaccinations in a global society

This paper discusses the complicated circumstances surrounding an individual's ability or choice to vaccinate either themselves or their children. Included is a section with a condensed history of vaccines, as well as a section describing their mechanism of action – providing background on how vaccines work within the human body. This paper also looks at factors such as a patient's relationship with their primary care provider, their socioeconomic status, education level, and even geographic location to nearby resources and how each impacts their ability to vaccinate. Incorporated within this paper are also the arguments of those opposed to vaccines and a rebuttal from myself arguing their importance.Honors CollegeThesis (B.?

Asymptotically Universal Unipotent Groups

We introduce the class of asymptotically universal unipotent groups, and show that they simultaneously satisfy certain "genericity" and "rigidity" properties that in combination render them very useful in the study of general wound unipotent groups. As an illustration of their utility, we present two applications: We prove that nonsplit smooth unipotent groups over (infinite) finitely-generated fields have infinite first cohomology; and we show that every commutative p-torsion wound unipotent group over a field of degree of imperfection 1 is the maximal unipotent quotient of a commutative pseudo-reductive group, thus partially answering a question of Totaro.Comment: 58 page

Moduli Spaces of Morphisms Into Solvable Algebraic Groups

We construct (in significant generality) moduli spaces representing the functor of morphisms from a scheme into a solvable algebraic group.Comment: 43 page