Maximal representations of uniform complex hyperbolic lattices in exceptional Hermitian Lie groups

We complete the classification of maximal representations of uniform complex hyperbolic lattices in Hermitian Lie groups by dealing with the exceptional groups ${\rm E}_6$ and ${\rm E}_7$. We prove that if $\rho$ is a maximal representation of a uniform complex hyperbolic lattice $\Gamma\subset{\rm SU}(1,n)$, $n>1$, in an exceptional Hermitian group $G$, then $n=2$ and $G={\rm E}_6$, and we describe completely the representation $\rho$. The case of classical Hermitian target groups was treated by Vincent Koziarz and the second named author (arxiv:1506.07274). However we do not focus immediately on the exceptional cases and instead we provide a more unified perspective, as independent as possible of the classification of the simple Hermitian Lie groups. This relies on the study of the cominuscule representation of the complexification of the target group. As a by-product of our methods, when the target Hermitian group $G$ has tube type, we obtain an inequality on the Toledo invariant of the representation $\rho:\Gamma\rightarrow G$ which is stronger than the Milnor-Wood inequality (thereby excluding maximal representations in such groups).Comment: Comments are welcome

On stratified Mukai flops

We construct a resolution of stratified Mukai flops of type A, D, E_{6, I} by successively blowing up smooth subvarieties. In the case of E_{6, I}, we construct a natural functor which induces an isomorphism between the Chow groups.Comment: use diagrams.st

The Road Not Taken: John Brown Francis and the Dorr Rebellion

In this contextualizing essay, Dr. Erik J. Chaput and Russell DeSimone examine historical opposing views to Providence attorney Thomas Wilson Dorr and his attempt to reform the state\u27s archaic governing structure in the spring of 1842. Chief among these views is that of former Governor John Brown Francis, who urged both sides to find a compromise with each other. The essay, along with a collection of letters it accompanies on our Dorr Rebellion Letters project site, elucidates how the moderate faction within the Law and Order party; had this moderate voice been heeded Rhode Island’s Dorr Rebellion would have turned out quite differently and that there were alternative approaches that politicians might have taken. The Dorr Rebellion Project http://library.providence.edu/dorr The Dorr Letters Project http://library.providence.edu:8080/xtf/index.htm

Dorr Rebellion Project Selected Bibliography

An annotated and traditional bibliography of research materials utilized by Dr. Erik J. Chaput and Rhode Island scholar Russell J. DeSimone in creating the script for The Dorr Rebellion short-form documentary and other resources on the Dorr Rebellion Project website. For those resources which are open access, an access link has been provided within the document. Visit the Dorr Rebellion Project website for more information: http://library.providence.edu/dorr

Stability of restrictions of cotangent bundles of irreducible Hermitian symmetric spaces of compact type

It is known that the cotangent bundle $\Omega_Y$ of an irreducible Hermitian symmetric space $Y$ of compact type is stable. Except for a few obvious exceptions, we show that if $X \subset Y$ is a complete intersection such that $Pic(Y) \to Pic(X)$ is surjective, then the restriction $\Omega_{Y|X}$ is stable. We then address some cases where the Picard group increases by restriction.Comment: Results and exposition improve