Mathematical Sciences: Research Experience in Computational Group Theory
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{'SignBlockName': 'John V. Ryff', 'PO_EMAI': None, 'PO_PHON': None}
This award will provide support for an REU site award                      supporting six students who will be engaged in mathematical                     research combining elements of abstract algebra - group theory -                with concepts from probability theory.  The primary tool                        underlying the work is the high level programming language CAYLEY               designed around the algebraic concepts of structure, set and                    mapping which uses an extensive data base of group theoretic and                geometric information.   The program allows users to define                     structures from which one may then extract information.                              Problems which will confront the students fall into two                    classes.  The first concerns what are called typical values in                  sampling theory, focusing on the amount of information about                    population means that one can obtain from information about                     subsample means (typical values).  With respect to symmetric                    differences, the subsamples may form a group.  The group                        structure is both necessary and sufficient to produce the typical               values.  The second class of problems concerns group structures                 which are not abelian but allow for quantitative studies of how                 near or far the groups are from being abelian.  There are many                  questions one can pursue in this area which can lead to new                     discoveries about existing groups as well as an appreciation for                the fundamental nature of group concepts such as cosets,                        conjugacy classes and subgroups.
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{'Code': '1260', 'Text': 'INFRASTRUCTURE PROGRAM'}
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