Sporadic Groups - Prof. Richard Borcherds - The Archimedeans

Prof. Richard Borcherds received a Fields medal in 1998. He is most famous for proving Monstrous Moonshine, a conjecture of John Conway and Simon Norton relating the Monster group to modular forms. Professor Borcherds' work has also played an important role in Quantum Field Theory and other areas of physics.

The longest published proof in mathematics, covering maybe around 20000 pages, is the classification of finite simple groups. It shows that every finite simple group is either contained in one of 18 infinite families, or is one of 26 exceptions called the sporadic groups, ranging in size from the Mathieu group M11 with 7920 elements to the Fischer-Griess monster group with 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000 elements. This talk will describe some of these sporadic groups.

No prerequisites are required, but it would be helpful to know what a group is.

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