Commensurated subgroups of arithmetic groups, totally disconnected groups and adelic rigidity

Investigations into and around a 30-year old conjecture of Gregory Margulis and Robert Zimmer on the commensurated subgroups of S-arithmetic groups.Comment: 50 page

Improving U.S. Housing Finance Through Reform of Fannie Mae and Freddie Mac: Assessing the Options

Presents criteria for evaluating proposals for reforming the two government-sponsored enterprises. Outlines the key arguments for their structural strengths and weaknesses, a framework and goals for reform, and features of specific proposals to date

New Fellow: Robert A. Willis, Jr.

Robert A. Willis, Jr. has been named Fellow of the Virginia Academy of Science. He has been an active member of the Virginia Academy of Science and the Association of Departments of Computer, Information Science/Engineering at Minority Institutions (ADMI) for nearly fifteen years

The Nub of an Automorphism of a Totally Disconnected, Locally Compact Group

To any automorphism, $\alpha$, of a totally disconnected, locally compact group, $G$, there is associated a compact, $\alpha$-stable subgroup of $G$, here called the \emph{nub} of $\alpha$, on which the action of $\alpha$ is topologically transitive. Topologically transitive actions of automorphisms of compact groups have been studied extensively in topological dynamics and results obtained transfer, via the nub, to the study of automorphisms of general locally compact groups. A new proof that the contraction group of $\alpha$ is dense in the nub is given, but it is seen that the two-sided contraction group need not be dense. It is also shown that each pair $(G,\alpha)$, with $G$ compact and $\alpha$ topologically transitive, is an inverse limit of pairs that have `finite depth' and that analogues of the Schreier Refinement and Jordan-H\"older Theorems hold for pairs with finite depth