应用数学哲学博士（组合）

组合学涉及对离散对象的一般研究。关于此类对象的推理贯穿数学和科学。例如，涉及解码基因组和系统发育树的主要生物学问题在很大程度上是组合的。量子引力的研究人员已经开发出深层的组合方法来评估积分，并且统计力学中的许多问题都离散化为组合问题。2006年的四枚菲尔兹奖章中有三枚是由于与组合学密切相关的工作而被授予的：Okounkov的关于随机矩阵的研究和Kontsevich的猜想，Tao的关于算术级数质数的研究以及Werner的渗滤研究。在过去的四十年中，我们的部门一直处于组合技术的前沿。已故的吉安·卡洛·罗塔（G
Combinatorics involves the general study of discrete objects. Reasoning about such objects occurs throughout mathematics and science. For example, major biological problems involving decoding the genome and phylogenetic trees are largely combinatorial. Researchers in quantum gravity have developed deep combinatorial methods to evaluate integrals, and many problems in statistical mechanics are discretized into combinatorial problems. Three of the four 2006 Fields Medals were awarded for work closely related to combinatorics: Okounkov's work on random matrices and Kontsevich's conjecture, Tao's work on primes in arithmetic progression, and Werner's work on percolation. Our department has been on the leading edge of combinatorics for the last forty years. The late Gian-Carlo Rota is regarded as the founding father of modern enumerative/algebraic combinatorics, transforming it from a bag of ad hoc tricks to a deep, unified subject with important connections to other areas of mathematics. Our department has been the nexus for developing connections between combinatorics, commutative algebra, algebraic geometry, and representation theory that have led to the solution of major long-standing problems. We are also a leader in extremal, probabilistic, and algorithmic combinatorics, which have close ties to other areas including computer science.