Computability, Logic and Complexity

9602579海岸 该奖项将支持首席研究员，教授理查德海岸，数学系，康奈尔大学，和两个初级研究员，教授彼得Cholak，数学系，圣母大学，和教授安德烈Nies，数学系，芝加哥大学，在三年内前往新西兰。 在新西兰，他们将与维多利亚大学逻辑组的同事，特别是罗德尼唐尼教授，以及奥克兰大学的同事，包括巴赫迪尔M。Khoussainov在康奈尔大学担任助理教授后，最近上任。 他们将各自研究递归理论中的一些主题，这些主题由研究计算如何与逻辑，数学和计算机科学的各个领域相互作用的共同主题联合起来。 大部分的工作将通过应用可计算性理论的方法，如优先方法和其他逻辑工具，如编码理论，在其他数学设置的有效性问题的研究来完成。 该项目结合了美国三个主要逻辑研究小组的优势，以及位于惠灵顿的维多利亚大学太平洋盆地的一个主要逻辑研究中心。

9602579 Shore This award will support the travel of the principal investigator, Professor Richard Shore, Department of Mathematics, Cornell University, and two junior investigators, Professor Peter Cholak, Department of Mathematics, University of Notre Dame, and Professor Andre Nies, Department of Mathematics, University of Chicago, to New Zealand over a three year-period. In New Zealand, they will work with colleagues in the logic groups at Victoria University, notably Professor Rodney Downey, and at Auckland University, including Dr. Bakhadyr M. Khoussainov who recently took up his position after serving as an Assistant Professor at Cornell University. They will each work on a number of topics in recursion theory united by a common theme of studying how computation interacts with various areas of logic, mathematics and computer science. Most of the work will be done by applying the methods of computability theory such as the priority method and other tools of logic such as the coding theories to the study of effectiveness issues in other mathematics settings. This project combines the strengths of three of the leading U.S. groups in logic with one of the leading centers of logic research in the Pacific Basin at Victoria University in Wellington.