Joint Colloquium: Ronan -- Symmetries and the Monster

This talk will describe the quest to find all the basic building blocks

for finite groups - the so-called ’finite simple groups’. Galois was the

first to find non-abelian examples, and many more were created later,

particularly using the work of Sophus Lie. By the early 1960s all the

known ones were either of ’Lie-type’ or one of five exceptions

discovered a hundred years earlier. Were there any more, and could we

find a complete list? 



A way forward was found using work of Richard Brauer, and the great

theorem of Walter Feit and John Thompson. While Thompson was advancing

these new methods, Zvonimir Janko, a Croatian mathematician working in

Australia, surprised the world with a very strange exceptional group,

the first one for a hundred years, and it really set the cat among the

pigeons. 



Further new exceptions came thick and fast, and they were called

"sporadic groups". We shall run through some of the highpoints,

including the Leech Lattice and the largest sporadic group - dubbed the

Monster - which turned out to reveal strange ’moonshine’ connections

between number theory and mathematical physics. 



The talk will include personal reminiscences and stories told me at

first hand. Some but not all of these are in my book of the same title,

published by Oxford University Press-see

http://www.math.uic.edu/~ronan/symmetryandthemonster. 


Mark Ronan -- University of Illinois at Chicago