Mathematical Sciences: Finite Groups: Permutation Representations, Generation and Monodromy Groups

小行星96223011 该奖项支持R. Guralnick在代数的许多不同领域工作。他将特别关注连接原始置换群的其他问题，代数，几何和数论，包括问题的多项式在有限领域。他还将研究如何生成有限简单群和交换环上对称矩阵的特征值的问题。 这是代数的一个分支，叫做群论。 群论可以看作是抽象的对称性研究。因此，它直接应用于物理和化学领域。许多群论也直接与编码理论中的问题联系在一起，因此与数据传输中的纠错这一非常实际的问题有着直接的关系。

96223011 Guralnick This award supports the research of Professor R. Guralnick to work in many diverse areas of algebra. He will be particularly concerned with connecting primitive permutation groups to other questions in algebra, geometry and number theory including problems of polynomials over finite fields. He will also study questions of how to generate finite simple groups and the eigenvalues of symmetric matrices over commutative rings. This is research in the subfield of algebra called group theory. Group theory can be though of as the study of symmetry in the abstract. As such, it has direct applications to areas of physics and chemistry. Much of group theory also connects directly to problems in coding theory and so has a direct bearing on the very practical problem of error correcting in data transfer.