Constructing Homogeneous Gorenstein Ideals

In 1983 Kustin and Miller introduced a construction of Gorenstein ideals in local Gorenstein rings, starting from smaller such ideals. We review and modify their construction in the case of graded rings and discuss it within the framework of Gorenstein liaison theory. We determine invariants of the constructed ideal. Concerning the problem of when a given Gorenstein ideal can be obtained by the construction, we derive a necessary condition and exhibit a Gorenstein ideal that can not be obtained using the construction

Effective Field Theory for Top and Weak Boson Physics

Effective field theory is the ideal framework for discussing top and weak boson properties. We discuss the application of this framework to top physics at both tree level and one loop. We consider weak boson pair production within an effective field theory framework, and argue that one need not be concerned with the violation of unitarity bounds at energies beyond the region where there are data.Comment: 3 pages, 4 figures. Talk presented at the Hadron Collider Physics Symposium 2011 (HCP 2011), Paris, France, November 14-18, 201

New C*-completions of discrete groups and related spaces

Let $\Gamma$ be a discrete group. To every ideal in \ell^{\infty}(\G) we associate a C$^*$-algebra completion of the group ring that encapsulates the unitary representations with matrix coefficients belonging to the ideal. The general framework we develop unifies some classical results and leads to new insights. For example, we give the first C$^*$-algebraic characterization of a-T-menability; a new characterization of property (T); new examples of "exotic" quantum groups; and, after extending our construction to transformation groupoids, we improve and simplify a recent result of Douglas and Nowak.Comment: 13 page