Mathematical Computation in Analysis and Number Theory

布朗大学数学系将购买计算机设备，包括工作站、网络硬件、编程和符号代数软件，这些设备将专门用于支持数学科学的研究。该设备将用于几个研究项目，特别包括：(1)波动现象的研究，非线性流体动力学中与自由面问题有关的奇异积分的数值计算，线性波的散射频率，以及非线性色散波的不稳定解；(2)数论和算术几何中的各种问题，如Weerstrass点的算术性质、p-adic动力系统及其不动点所生成的场、数域上椭圆曲线的正则高度、K3曲面的丢番图几何等：(3)椭圆微分算子的边值问题和特征值问题。

The Department of Mathematics at Brown University will purchase computer equipment consisting of workstations, networking hardware, and programming and symbolic algebra software which will be dedicated to support research in the mathematical sciences. The equipment will be used for several research projects, including in particular: (1) the study of wave phenomena, the numerical computation of singular integrals related to free surface problems in non-linear fluid dynamics, the scattering frequency of linear waves, and the unstable solutions of nonlinear dispersive waves; (2) various problems in number theory and arithmetic geometry, such as arithmetic properties of Weierstrass points, p-adic dynamical systems and the fields generated by the fixed points of such systems, canonical heights on elliptic curves over number fields, and the Diophantine geometry of K3 surfaces; (3) boundary value problems and eigenvalue problems for elliptic differential operators.