Abstract:
Conformal extensions of Levy-Leblond's Carroll group, based on geometric properties analogous to those of Newton-Cartan space-time are proposed. The extensions are labelled by an integer $k$. This framework includes and extends our recent study of the Bondi-Metzner-Sachs (BMS) and Newman-Unti (NU) groups. The relation to Conformal Galilei groups is clarified. Conformal Carroll symmetry is illustrated by "Carrollian photons". Motion both in the Newton-Cartan and Carroll spaces may be related to that of strings in the Bargmann space.

Abstract:
I argue that the Carroll-Chen cosmogenic model does not provide a plausible scientific explanation of our universe's initial low-entropy state.

Abstract:
The Bondi-Metzner-Sachs (BMS) group is shown to be the conformal extension of Levy-Leblond's "Carroll" group. Further extension to the Newman-Unti (NU) group is also discussed in the Carroll framework.

Abstract:
The Andrews-Curtis conjecture claims that every balanced presentation of the trivial group can be reduced to the standard one by a sequence of ``elementary transformations" which are Nielsen transformations augmented by arbitrary conjugations. It is a prevalent opinion that this conjecture is false; however, not many potential counterexamples are known. In this paper, we show that some of the previously proposed examples are actually not counterexamples. We hope that the tricks we used in constructing relevant chains of elementary transformations will be useful to those who attempt to establish the Andrews-Curtis equivalence in other situations. On the other hand, we give two rather general and simple methods for constructing balanced presentations of the trivial group; some of these presentations can be considered potential counterexamples to the Andrews-Curtis conjecture. One of the methods is based on a simple combinatorial idea of composition of group presentations, whereas the other one uses "exotic" knot diagrams of the unknot. We also consider the Andrews-Curtis equivalence in metabelian groups and reveal some interesting connections of relevant problems to well-known problems in K-theory.

Abstract:
In [4]: `The Riley slice of Schottky space', (Proc. London Math. Soc. 69 (1994), 72-90), Keen and Series analysed the theory of pleating coordinates in the context of the Riley slice of Schottky space R, the deformation space of a genus two handlebody generated by two parabolics. This theory aims to give a complete description of the deformation space of a holomorphic family of Kleinian groups in terms of the bending lamination of the convex hull boundary of the associated three manifold. In this note, we review the present status of the theory and discuss more carefully than in [4] the enumeration of the possible bending laminations for R, complicated in this case by the fact that the associated three manifold has compressible boundary. We correct two complementary errors in [4], which arose from subtleties of the enumeration, in particular showing that, contrary to the assertion made in [4], the pleating rays, namely the loci in R in which the projective measure class of the bending lamination is fixed, have two connected components.

Abstract:
We relate the Andrews-Curtis conjecture to the triviality problem for balanced presentations of groups using algorithms from 3-manifold topology. Implementing this algorithm could lead to counterexamples to the Andrews-Curtis conjecture.

Abstract:
The well known Andrews-Curtis Conjecture [2] is still open. In this paper, we establish its finite version by describing precisely the connected components of the Andrews-Curtis graphs of finite groups. This finite version has independent importance for computational group theory. It also resolves a question asked in [5] and shows that a computation in finite groups cannot lead to a counterexample to the classical conjecture, as suggested in [5].

Abstract:
Adolph F. Bandelier (1840-1914) is best known for his work in the Southwestern United States, particularly among the pueblos and prehistoric sites of the Rio Grande area, although he did extensive field and archival research in Mexico and South America as well. Self-taught, like most of his contemporaries, his research included archaeology, ethnology, history, and geography, plus a serious interest in botany, zoology, and meteorology. Bandelier was born in Bern, Switzerland, but when he was eight his family moved to the largely Swiss settlement of Highland, Illinois, 30 miles east of St. Louis, where he attended school, was tutored privately, and taught by his well educated mother. He mastered German and English, as well as his native French, and later added Spanish and Latin. For many years he worked in his father's general store, finally, at the age of forty, making the difficult decision to devote himself to scholarship rather than business. In 1869 at the St. Louis Mercantile Library he had begun the study of prehistoric Mexican cultures. He met Lewis Henry Morgan on a trip to the east and for many years was greatly influenced by his view of cultural evolution, but he.remained far more fact oriented than concerned with theory. Bandelier's first major work, "On the Art of War and Mode of Warfare of the Ancient Mexicans," was published in 1877 by the Peabody Museum of Harvard.

Abstract:
The paper discusses the Andrews-Curtis graph of a normal subgroup N in a group G. The vertices of the graph are k-tuples of elements in N which generate N as a normal subgroup; two vertices are connected if one them can be obtained from another by certain elementary transformations. This object appears naturally in the theory of black box finite groups and in the Andrews-Curtis conjecture in algebraic topology. We suggest an approach to the Andrews-Curtis conjecture based on the study of Andrews-Curtis graphs of finite groups, discuss properties of Andrews-Curtis graphs of some classes of finite groups and results of computer experiments with generation of random elements of finite groups by random walks on their Andrews-Curtis graphs.

Abstract:
On March 14, 1998, Utah Governor Michael O. Leavitt signed Senate Bill 149 which adopted the Nursing Regulation Interstate Compact. The Division of Occupational and Professional Licensing and the Utah Board of Nursing have been studying the issues of multistate practice and licensure since 1996. Several issues provided the necessary impetus to precede with changing nursing regulation including the changing delivery of nursing services. This article describes the reasons why Utah chose to adopt the compact language and the process that was followed. Advice to states who are interested in adopting the mutual recognition model of nursing regulation is also provided.