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

这笔赠款支持J·皮拉教授从事数论的研究。特别是，他希望研究关于亏格2的超椭圆曲线的雅可比约化的点数的算法。他还打算致力于获得位于正方形内的曲线上的积分格点的数目的改进的界。这是数论领域的研究。数论始于整数和诸如一个整数被另一个整数整除的问题。它是最古老的数学领域之一，最初是出于纯粹的美学原因。然而，在过去的半个世纪里，它已经成为计算机科学的新算法和电子产品的新纠错码等领域的重要工具。

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.