Mathematical Sciences: Experimental Mathematics

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Ten students will receive support from this Research Experiences for Undergraduates award. They will work under the direction of three faculty advisors for a period of two summer months. In the preceding award, institutional support for five additional students was provided; a similar arrangement is anticipated with the receipt of this grant. Much of the experimental work involves computational work which will be carried out in the Mathematics Computer Assisted Learning Center. The center has excellent computer and software resources available to the researchers. The primary theme used during the first year to exemplify the experimental nature of mathematical research will be computational and combinatorial group theory. Here computers have not only been used to check examples and discover patterns but also to settle problems which have been reduced to a finite number of cases. After an orientation period, students will begin work on problems concerning the Mobius function of finite groups, finding the number of reduced expressions in the Coxeter generators for elements of the affine Weyl group and, along a more geometric line, to look at the Hurwitz problem for finite simple groups of small order. This final area concerns the problem of determining all possible genera of closed, orientable surfaces which admit a symmetry by the group.