Remarks on Non-Abelian Cohomology of Proalgebraic Groups

These are detailed notes on a variant of the non-abelian cohomology developed by Minhyong Kim in arXiv:0409456 (published in Invent. Math.) to study rational points of varieties over number fields. The current variant is used in arXiv:1001.5008 to study rational points of the restriction of the universal curve to the generic point of M_{g,n}.Comment: 14 pages. The main result has been strengthened by removal of the connectedness assumption. Some minor errors and typos have been fixe

Normal Functions and the Geometry of Moduli Spaces of Curves

In this paper normal functions (in the sense of Griffiths) are used to solve and refine geometric questions about moduli spaces of curves. The first application is to a problem posed by Eliashberg: compute the class in the cohomology of M_{g,n}^c of the pullback of the zero section of the universal jacobian along the section that takes [C;x_1,...,x_n] to Sum d_j x_j in Jac (C), where d_1 + ... + d_n = 0. The second application is to slope inequalities of the type discovered by Moriwaki. There is also a discussion of height jumping and its relevance to slope inequalilties.Comment: Updated to published version. Also added publication informatio

Milliken v. Green: Breaking the Legislative Deadlock

A chronicle of efforts at educational finance reform in Michigan in which the state judiciary initially ruled that the deductible-millage system was unconstitutional in Milliken V Green later dismissed the case, but in the process stimulated the legislature to move toward reform