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

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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.