Combinatorial problems arising in finite group theory, 3-manifold topology and other areas

DMS-0300483 Shareshian，JohnAbstract标题：出现在有限群论、3-流形拓扑学和其他领域的组合问题。Shareshian研究组合问题，并在其他领域应用。他与R.Roberts和M.Stein的合作涉及到使用树状对象上的群作用理论来研究三维流形的叶层。他与R。Guralnick关于对称群和交错群Onk-集的作用被用来研究Riemann球面的分支覆盖的单角群。他与M.Wach等人在图和超图复形方面的工作在交换代数、有限群论和纽结理论中都有应用。他在子群格中区间序复形的拓扑方面的工作旨在为解决泛代数中一个长期存在的问题提供一种新的途径。主要研究人员在组合学中的各种问题上工作。大体上，组合学是对离散的(通常是有限的)数学对象的研究，这些对象允许相当基本的描述，但其结构可能非常复杂。通常情况下，其他学科(如计算机科学、电气工程和生物)以及其他更技术性和抽象的数学领域的问题可以归结为组合问题。

DMS-0300483Shareshian, JohnAbstractTitle: Combinatorial problems arising in finite group theory, 3-manifoldTopology and other areas.Shareshian works on combinatorial problems with applicationsin other fields. His joint work with R. Roberts and M. Steininvolves using the theory of group actions on tree-like objectsto investigate foliations of 3-manifolds. His joint work withR. Guralnick on actions of symmetric and alternating groups onk-sets is used to investigate monodromy groups of branchedcoverings of the Riemann sphere. His joint work with M. Wachsand others on graph and hypergraph complexes has applicationsin commutative algebra, finite group theory and knot theory.His work on topology of order complexes of intervals in subgrouplattices is intended to provide a new approach to a longstandingproblem in universal algebra.The principal investigator works on various problems incombinatorics. Roughly, combinatorics is the study of discrete(often finite) mathematical objects which admit fairly elementarydescriptions but whose structure can be quite complicated. It isoften the case that problems in other disciplines (such as computerscience, electrical engineering and biology) and other moretechnical and abstract areas of mathematics can be reduced tocombinatorial problems.