MATHEMATICAL SCIENCES: Galois Representations

9400833 拉森 该奖项资助迈克尔·拉森教授对基本群的单值表示的研究，特别是当它们出现在数论中时。 Larsen教授将尝试在特定情况下计算单值群，并研究基础数据变化引起的变化。 他希望能够构建的例子中的monodromy组是预先规定的，一个逆问题的基础上的不变量的诱导表示。 这是算术代数领域的研究 几何学是一门结合了代数和几何学技巧的学科。 几何学和数论在其最初的提法中， 代数几何处理的图形，可以定义在 平面由最简单的方程，即多项式。Number 理论开始于整数， 一个整数被另一个整数整除。这两个看似相距甚远的主题，实际上相互影响， 但在过去的四分之一世纪， 影响力大增。其结果是增加了对这两个数学领域的理解。

9400833 Larsen This award funds the investigations of Prof. Michael Larsen into monodromy representations of fundamental groups especially as they arise in number theory. Prof. Larsen will attempt to compute monodromy groups in particular cases and study variations caused by changes in the base data. He would like to be able to construct examples where the monodromy group is prescribed beforehand, an inverse problem based on the invariants of the induced representation. 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 result has been an increased understanding of both areas of mathematics.