Random Partitions, Random Matrices, and Combinatorics of Moduli Spaces of Curves

曲线模空间的随机划分、随机矩阵和组合

• 批准号: 0100593
• 负责人: Andrei Okounkov
• 金额: $ 8.85万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-07-01 至 2004-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0100593&HistoricalAwards=false
• 关键词: Random; Partitions; Matrices; Combinatorics; Moduli

The proposer is going to study a number of interconnected combinatorial problems related, on the one hand, to exact or asymptotic enumeration of branched coverings of one surface by another and, on the other hand, to exact or asymptotic evaluation of various sums over partitions. These problems arise both from enumerative geometry of the moduli spaces of curves (and related moduli spaces) and from connection with random matrices. If solved, these problems will lead to important applications to algebraic geometry, ergodic theory, and other fields, and will also substantially further our present understanding of the interaction between geometry of the moduli spaces and combinatorics of random matrices and partitions.

作者将研究一些相互关联的组合问题，这些问题一方面与一个曲面上分支覆盖的精确或渐近计数有关，另一方面与分割上各种和的精确或渐近计算有关。这些问题既源于曲线的模空间的计数几何(以及相关的模空间)，也源于与随机矩阵的联系。如果这些问题得到解决，这些问题将在代数几何、遍历理论和其他领域中得到重要的应用，并将极大地促进我们目前对模空间几何与随机矩阵和划分的组合学之间相互作用的理解。