EVENT: Mathematics and Statistics Colloquium

Symmetry appears to be a guiding principle underlying most laws in science. For example, nature uses symmetry for compact encoding of genetic information, and postulating such "genetic economy" led Crick and Watson to discover the particular icosahedral symmetry of viruses. Within mathematics, we encode the symmetries of any structure as a group, and the groups I study are those acting on huge and complex (but still finite) structures, such as the enormous mathematical graphs underpinning large computer networks. The classification of the finite simple groups (CFSG), said to be one of the greatest achievements of twentieth century mathematics, had a profound impact on research in symmetry. The finite simple groups are the building blocks for finite groups, and many problems involving finite symmetric structures are reduced to questions which can be solved using the simple group classification. How does this work? What information about simple groups is needed? What if it's not available? It will be challenging to describe in one hour -- but let me try.