MATHEMATICAL SCIENCES: Galois Representations

9400833 Larsen该奖项资助Michael Larsen教授对基本群的单态表示的研究，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组，并研究由基础数据变化引起的变化。他希望能够构造一些单群是预先规定的例子，一个基于诱导表示的不变量的逆问题。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。其结果是加深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.