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A uniform approach to computations with finite groups
We survey the efforts to computations with "concrete" representations of groups, input by a generating set of permutations or matrices. The basic problems are to determine the order of the input group, to set up a data structure which enables us to test whether any given permutation or matrix is in the group, and obtain structural information such as a composition series. Groups arise whenever symmetries of mathematical objects are studied, so these investigations are relevant and applicable in many areas of mathematics.
Particular attention will be given to a recent approach to treat permutation groups and matrix groups uniformly, within the same framework. We use a mixture of methods from group theory, combinatorics, probability theory, and computer science.
Akos Seress is a leader of his field: computational group theory and algebraic algorithms. He has 69 publications, including a monograph. (Permutation Group Algorithms. Cambridge Tracts in Mathematics, 152. Cambridge University Press, Cambridge, 2003.) This is a relatively new topic, full of problems (accessible to graduate students) and with famous results that rejuvenated group theory. Akos Seress is an invited speaker for the next ICM 2006.
Thursday, October 27, 2005, 245 Altgeld Hall, 4:00 p.m.
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