A soft Oka principle for proper holomorphic embeddings of open Riemann surfaces into (C∗)2(\mathbb{C}^*)^2

Let $X$ be an open Riemann surface. We prove an Oka property on the approximation and interpolation of continuous maps $X \to (\mathbb{C}^*)^2$ by proper holomorphic embeddings, provided that we permit a smooth deformation of the complex structure on $X$ outside a certain set. This generalises and strengthens a recent result of Alarcon and Lopez. We also give a Forstneric-Wold theorem for proper holomorphic embeddings (with respect to the given complex structure) of certain open Riemann surfaces into $(\mathbb{C}^*)^2$

The Impact of a National Science Foundation Collaborative for Excellence in Teacher Preparation on an Undergraduate Chemistry Course for Non-Chemistry Science Majors

In 1999 and 2000 Chemistry 312: Analytical Chemistry for non-chemistry science majors (taken in the junior or senior year), was revised as a result of the instructor’s involvements in the Center for Excellence in Teacher Preparation project and an NSF equipment grant. Changes included the introduction of a K-12 teaching requirement, more emphasis on co-operative learning and on inquiry-based exercises. These latter two pedagogical practices had more impact on the laboratory activities than on the classroom activities. Students in the laboratory were assigned defined roles in the groups and all groups undertook a three-week research project. Students’ responses to the teaching requirement were (with a few exceptions in a class of over forty) positive, and several students identified themselves as future teachers. Responses to the group work associated with the laboratory and several homework exercises were less uniformly positive, with a significant number of students articulating a concern that their grades were compromised by the presence of weaker students in the groups. The grades awarded, the overall percentages and the exam scores of the students were compared for the years 1998, 1999, and 2000. There was a significant improvement in the overall percentages (and the exam scores) between 1998 and 1999, and between 1998 and 2000. Had the thresholds for the awarding of letter grades not been increased for 2000, there would have been 31 A’s awarded to the 44 students who completed the course

A strong Oka principle for embeddings of some planar domains into CxC*

Gromov, in his seminal 1989 paper on the Oka principle, introduced the notion of an elliptic manifold and proved that every continuous map from a Stein manifold to an elliptic manifold is homotopic to a holomorphic map. We show that a much stronger Oka principle holds in the special case of maps from certain open Riemann surfaces called circular domains into CxC*, namely that every continuous map is homotopic to a proper holomorphic embedding. An important ingredient is a generalisation to CxC* of recent results of Wold and Forstneric on the long-standing problem of properly embedding open Riemann surfaces into C^2, with an additional result on the homotopy class of the embeddings. We also give a complete solution to a question that arises naturally in Larusson's holomorphic homotopy theory, of the existence of acyclic embeddings of Riemann surfaces with abelian fundamental group into 2-dimensional elliptic Stein manifolds.Comment: 25 page

Optical Synoptic Telescopes: New Science Frontiers

Over the past decade, sky surveys such as the Sloan Digital Sky Survey have proven the power of large data sets for answering fundamental astrophysical questions. This observational progress, based on a synergy of advances in telescope construction, detectors, and information technology, has had a dramatic impact on nearly all fields of astronomy, and areas of fundamental physics. The next-generation instruments, and the surveys that will be made with them, will maintain this revolutionary progress. The hardware and computational technical challenges and the exciting science opportunities are attracting scientists and engineers from astronomy, optics, low-light-level detectors, high-energy physics, statistics, and computer science. The history of astronomy has taught us repeatedly that there are surprises whenever we view the sky in a new way. This will be particularly true of discoveries emerging from a new generation of sky surveys. Imaging data from large ground-based active optics telescopes with sufficient etendue can address many scientific missions simultaneously. These new investigations will rely on the statistical precision obtainable with billions of objects. For the first time, the full sky will be surveyed deep and fast, opening a new window on a universe of faint moving and distant exploding objects as well as unraveling the mystery of dark energy.Comment: 12 pages, 7 figure