Mathematical Sciences: Diophantine Approximations of Algebraic Points

该奖项支持加州大学伯克利分校Paul Vojta教授对丢番图近似法的研究。Vojta博士的项目是扩展他在Nevanlinna理论和Diophantine近似理论之间已经产生的类比，以获得关于变量上有界度的代数点的信息。此外，他还希望将他对莫德尔-法尔廷斯定理的独立证明推广到高维的各种变化中。莫德尔-法尔廷斯定理是将他的观点应用于戴森对休-西格尔定理的锐化而产生的。这是算术代数几何领域的研究，是一门结合了代数几何和数论技术的学科。在其最初的公式中，代数几何处理的图形可以用最简单的方程，即多项式在平面上定义。数论始于整数和整数能否被整数整除之类的问题。这两个看似相距甚远的主题，实际上从最早的时代起就相互影响，但在过去的四分之一世纪中，相互影响大大增加。算术代数几何领域现在使用了所有现代数学的技术，并在其本身的边界之外产生了相应的影响。

This award supports the research in Diophantine approximations of Professor Paul Vojta of the University of California at Berkeley. Dr. Vojta's project is to extend his already-productive analogy between Nevanlinna Theory and Diophantine approximation theory, so as to get information on algebraic points of bounded degree on varieties. In addition, he hopes to generalize to varieties of higher dimension his independent proof of the Mordell-Faltings Theorem that arose from applying his viewpoint to Dyson's sharpening of the Thue-Siegel Theorem. This is research in the field of arithmetic algebraic geometry, a subject that combines the techniques of algebraic geometry and number theory. In its original formulation, algebraic geometry treated figures that could be defined in the plane by the simplest equations, namely polynomials. Number theory started with the whole numbers and such questions as divisibility of one whole number by another. These two subjects, seemingly so far apart, have in fact influenced each other from the earliest times, but in the past quarter century the mutual influence has increased greatly. The field of arithmetic algebraic geometry now uses techniques from all of modern mathematics, and is having corresponding influence beyond its own borders.