Arithmetic Groups

算术组

• 批准号: 0354731
• 负责人: Gregory Margulis
• 金额: $ 12.28万
• 依托单位: Yale University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-07-01 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0354731&HistoricalAwards=false
• 关键词: Arithmetic; Groups

We plan to study arithmetic groups for their own sake and for theirapplications to other branches of mathematics and computer science.Two central themes are the subgroup growth of arithmetic lattices and thecombinatorics of the simplicial complexes obtained by taking quotients ofBruhat-Tits buildings modulo arithmetic groups.Arithmetic groups are at the crossroads of several central areas ofmathematics: Lie groups, number theory, geometry and combinatorics.Their study can be carried out using a wealth of different methods andshed light on different directions. A previous work has led to theconstruction of Ramanujan graphs which turn out to have remarkableapplications to computer science and combinatorics. One of the goals ofthis research will be to study higher dimensional analogues with thehope of getting deeper applications.

我们计划研究算术群，是为了它们本身，也是为了它们在数学和计算机科学的其他分支中的应用。两个中心主题是算术格的子群增长和通过取Bruhat-Tits建筑的模算术群的商而得到的单纯复形的组合性。算术群处于数学的几个中心领域的十字路口：李群，数论，几何和组合学。它们的研究可以用许多不同的方法来进行，并揭示不同的方向。以前的一项工作导致了Ramanujan图的构造，它在计算机科学和组合学中有显著的应用。这项研究的目标之一将是研究更高维度的类似物，希望获得更深层次的应用。