Scientific Computing Research Environments for the Mathematical Sciences (SCREMS)

数学系和应用与计算数学专业建议购买一个计算集群，专门用于支持数学科学的计算研究。本研究将特别集中在以下领域：(1)分离磁成像数据中独立成分的新算法，以研究脑功能；(2)生物分子如何在不同构象之间获取和移动的动力学；(3)与椭圆曲线上的Goldfeld猜想（数论中著名的猜想）有关的解析秩的研究；(4)计算机辅助计数的尖角双曲3流形。这些项目都需要专门的设施，而Fine Hall目前还没有。从科学和教育的角度来看，拟议的项目位于不同学科之间的接口：功能磁共振成像项目的信号处理，统计学和心理学；第二项目应用数学和生物化学；3流形项目的拓扑和几何。这些项目的进展将影响到几个社区。此外，这些项目将成为ppi继续努力的一部分，将前沿研究带到课堂上的科学教育中，并吸引女性和其他代表性不足的群体进入数学领域。将组织新的课程和讨论会，以便数学界和科学界的更大一部分人能够通过拟议的设施接触到这些研究项目。

The Department of Mathematics and Program in Applied and Computational Mathematics proposes to purchase a computational cluster which will be dedicated to support computational research in mathematical sciences. This research will be concentrated in particular in the following areas: (1) new algorithms for the separation of independent components in magnetic imaging data to study brain function, (2) the dynamics of how bio-molecules acquire and move between different conformations, (3) study of the analytic rank in connection with the Goldfeld conjecture on elliptic curves (a well-known conjecture in number theory), and (4) computer-assisted enumeration of cusped hyperbolic 3-manifolds.Each of these projects require dedicated facilities that Fine Hall does not have currently. From a scientific and educational point of view, the proposed projects lie at the interfaces between different disciplines: signal processing, statistics and psychology for the fMRI project; applied mathematics and biochemistry for the second project; topology and geometry for the 3-manifold project. Progress on these projects will impact several communities. In addition, these projects will be part of the PIs' continuing effort on bringing frontier research to science education in the classrooms, as well as attracting women and other under-represented groups to the area of mathematics. New courses and discussion sessions will be organized so that a much larger part of the mathematical and scientific community will have access to these research projects through the proposed facility.