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

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