Bertram Kostant recently gave this talk at UCR: On Some Mathematics in Garrett Lisi's "E8 Theory of Everything" Abstract: A physicist, Garrett Lisi, has published a highly controversial, but fascinating, paper purporting to go beyond the Standard Model in that it unifies all 4 forces of nature by using as gauge group the exceptional Lie group E8. My talk, strictly mathematical, will be about an elaboration of the mathematics of E8 which Lisi relies on to construct his theory. You can see videos of this talk and lecture notes here: http://math.ucr.edu/home/baez/kostant/ If his talk is too tough, you might prefer the warmup talk I gave earlier that day. But, Kostant described some ideas whose charm is easy to appreciate: The dimension of E8 is 248 = 8 x 31. There is, in fact, a natural way to chop up E8 into 31 spaces of dimension 8. There is a nice way to see the product of two copies of the Standard Model gauge group sitting inside E8. The Standard Model gauge group is a subgroup of SU(5). There is also a nice way to see the product of two copies of SU(5) sitting inside E8. The dimension of SU(5) x SU(5) is 48, and 248 - 48 = 200. The adjoint action of SU(5) x SU(5) on the Lie algebra of E8 thus gives a 200-dimensional representation, and this is (5 x 10) + (5* x 10*) + (10 x 5) + (10* x 5*) Garrett Lisi's ideas have received serious criticism from Jacques Distler and others. I've included links to Lisi's paper and also Distler's comments. But, the work Kostant presents here is logically independent - beautiful math, regardless of its possible applications to physics. It makes heavy use of recent work on certain finite subgroups of E8, most notably GL(2,32) and (Z/5)^3. As Kostant said, "E8 is a symphony of twos, threes and fives".