Mathematical Sciences: Some Problems in Algorithmic Number Theory and Diophantine Equations

这笔赠款支持J.Pila教授的研究工作 在数论中。 特别是，他希望研究算法， 关于超椭圆的Jacobian约化的计数点 亏格曲线2. 他还打算努力改善 曲线上整格点个数的界 在广场内。 这是数论领域的研究。 Number 理论开始于整数和问题，如 一个整数被另一个整数整除。 它是其中的 最古老的数学领域，它最初是追求 纯粹的美学原因。 然而，在过去的半个世纪里， 它已成为开发新的 计算机科学算法和新的纠错码 electronics.

This grant supports the research of Professor J. Pila to work in number theory. In particular, he wishes to work on algorithms for counting points on the reductions of Jacobians of hyperelliptic curves of genus 2. He also intends to work on obtaining improved bounds for the number of integral lattice points on curves lying inside squares. This is research in the field of number theory. Number theory starts with the whole numbers and questions such as the divisibility of one whole number by another. It is among the oldest fields of mathematics and it was originally pursued for purely aesthetic reasons. However, within the last half century, it has become an essential tool in areas such as developing new algorithms for computer science and new error correcting codes for electronics.