I review the theoretical expectactions for the top-quark mass in a variety of models: the Standard Model, unified models (GUTs), low-energy supersymmetric models (SUSY), unified supersymmetric models (SUSY GUTs), supergravity models, and superstring models. In all instances I consider the constraints on the top-quark mass which arise by demanding that these theories be weakly interacting. This ...

Freeform modeling is an integral part of the geometric modeling and design process. Existing freeform modeling systems expect the user to be familiar with the geometric representation and user interface in order to model precisely and rapidly. As a result, modeling complex freeform geometries precisely and rapidly can be quite difficult. In this thesis, we address the problems manifested in cur...

We discuss the status of supersymmetric grand unified theories [SUSY GUTs] with regards to the observation of proton decay. In this talk we focus on SUSY GUTs in 4 dimensions. We outline the major theoretical uncertainties present in the calculation of the proton lifetime and then present our best estimate of an absolute upper bound on the predicted proton lifetime. Towards the end, we consider...

We discuss the status of supersymmetric grand unified theories [SUSY GUTs] with regards to the observation of proton decay. In this talk we focus on SUSY GUTs in 4 dimensions. We outline the major theoretical uncertainties present in the calculation of the proton lifetime and then present our best estimate of an absolute upper bound on the predicted proton lifetime. Towards the end, we consider...

I discuss an evolution of SUSY GUT model building, starting with the construction of 4d GUTs, to orbifold GUTs and finally to orbifold GUTs within the heterotic string. This evolution is an attempt to obtain realistic string models, perhaps relevant for the LHC. This review is in memory of the sudden loss of Julius Wess, a leader in the field, who will be sorely missed. PACS. PACS-key discribin...