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体，并将其应用于其他数学和计算机科学的其他分支。两个中央主题是算术晶格的亚组增长，以及通过将bruhat-tits buildings of Buildings组的定量组成的库存组成的单品组成的简单络合物的子组合。理论，几何学和组合学。可以使用各种不同的方法和不同方向上的灯光进行研究。 先前的工作导致了Ramanujan图的结构，这些图形对计算机科学和组合设备具有出色的plap依。这项研究的目标之一将是研究更深入的类似物，以获取更深的应用程序。