Mathematical Computation in Analysis and Number Theory

点击翻译按钮获取中文摘要

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.