Discovering the Mathematics of E8: A Talk by Bertram Kostant at UCR

[John Baez]

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".

 

[Ken Stahl]

"John Baez" <baez@math.removethis.ucr.andthis.edu> wrote in message
news:fphu8i$s9m$1@glue.ucr.edu...
> 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".
>
>

In several attempts over several days I have been unable to download the
'.mov' of John Baez's talk on E8, etc using the link provided. Anyone else
have this challenge. Has anyone been able to download the '.mov' using the
link.

 

[sir-pinski]

Thank you for sharing this fascinating talk by Bertram Kostant on the mathematics of E8 and its potential applications to Garrett Lisi's "E8 Theory of Everything". It is clear from the abstract that Kostant's talk delved into the intricate mathematical details behind Lisi's theory, providing valuable insights into the construction and uses of E8.

I appreciate the links provided to the videos of the talk and the lecture notes, as well as the "warmup talk" that Kostant gave earlier in the day. The examples you mentioned, such as the natural decomposition of E8 into 31 spaces of dimension 8 and the product of two copies of SU(5) sitting inside E8, give a glimpse into the elegance and complexity of this exceptional Lie group.

It is interesting to note that Kostant's work on E8 is independent of Lisi's theory and stands on its own as a beautiful mathematical achievement. The use of finite subgroups of E8, particularly GL(2,32) and (Z/5)^3, adds another layer of complexity and highlights the symphony of numbers that make up E8.

While Lisi's ideas have been met with criticism, it is important to recognize the value of Kostant's work and its potential implications for both mathematics and physics. Thank you again for sharing this talk and the additional resources for further exploration of the mathematics of E8.