WhY arent more people watching this video its literally by the dude who proved the monstrous moonshine conjecture and won the friggin fields medal for it😂
The channel is relatively new and does not get much promotion, the topics are difficult and first-time watcher may be tricked to think this is one of those incomprehensible "Hello today we discuss basics of XXX theory. Now we start with a simple XTDS-1 transformation on polymorphic Grassmann-Lyapunov magma with semi-unitary... *math math math math math math math math* here are some extremely long unintelligeble formulae *math math math math* goodbye " videos.
Because most of us, regardless of how much work we put in, will not be able to operate anywhere near this genius's ability so we might as well look at boobs instead. We can study chess all day long, after five years we'll still get crushed by Carlson so what's the point?
Thank you dear professor. I am a surgeon. I was bitten by the math bug last year due to stalwarts like you. Thanks for making me see beauty again in formal education.
This is a great talk, thanks for your effort. FYI there are some short sections where the audio track becomes distorted, and one or two where words cannot be understood. Its accessibility would be helped by subtitles to cover those sections.
Thanks a lot, Prof. Borcherds! I actually found your explanation of vertex algebras very useful, because I know quantum field theory, and could relate the axioms to the operator product expansion!
This monstrous moonshine stuff is really fascinating. I'm just trying to find the connection to sqrt(163) and the fine structure constant ε0 in physics. Someone mentioned it to me, but I can't recall the details. Borcherds might know more about it.
I believe "Vertex Operator Algebras and the Monster" (Frenkel, Lepowsky, Meurman) is a well-known book on this topic specifically. As he noted in the talk, "Vertex Algebras for Beginners" is an "introduction" to vertex algebras in general.
I got through the entire video, thought it was interesting, then months later watched the Numberphile video on the Monster group. "Hmm, that name 'Richard Borcherds' seems familiar"...
Hello smart people. If you understand this video I sincerely hope you are being paid well because I can’t imagine how many courses in math you’ve had to pay for
This is honestly understandable by someone with an undergraduate mathematics education with independent learning of group, representation, and algebraic vertex theory
about the algebra product, though. there are a few more identities involving the inner product. and when two vectors alternate as a(ac) = (aa)c. then all possible vectors b associate like a(bc) = (ab)c. in other words, alternativity implies associativity.
the inner product actually creates a symmetric **trilinear** form with the algebra product. in other words, the inner product (ab, c) = (a, bc) is invariant under all permutations of a, b, and c.
also, John H. Conway simplified the construction significantly by incorporating the Parker loop into the construction in order resolve the sign problem. he also incorporated the fixed vector into the algebra product by treating it as an identity element. he also used double covers and fourfold convers of **three** involution centralisers and the normaliser of a specific fourgroup in the monster. rather than treating the centraliser of a **single** involution, he took centralisers of **all three** involutions of the fourgroup, and constructed the monster as the group generated by the three matrix groups that **each centralise a different** involution in the fourgroup. and the "three" algebra products defined over them are actually one and the same.
Hi. Does there exist a mapping of a set of Monster symmetries to those that are compatible with Calabi-Yau manifolds? I'm wondering if any symmetry relations that exist in M might manifest in lower dimensions, some subgroup of M, as (at least roughly) symmetries of the Standard Model and/or those of spacetime? We've got this beautiful, complex group that exists and touches so many branches of maths, makes me wonder how much it and it mysteries might manifest.
So en.wikipedia.org/wiki/743_(number) or 744 could be zero, but just not as groupie. Root(744)? I vaguely remember discriminants of the 44 elliptics of character 1 modulo 3 being 18 of them. ...
WhY arent more people watching this video its literally by the dude who proved the monstrous moonshine conjecture and won the friggin fields medal for it😂
The channel is relatively new and does not get much promotion, the topics are difficult and first-time watcher may be tricked to think this is one of those incomprehensible "Hello today we discuss basics of XXX theory. Now we start with a simple XTDS-1 transformation on polymorphic Grassmann-Lyapunov magma with semi-unitary... *math math math math math math math math* here are some extremely long unintelligeble formulae *math math math math* goodbye " videos.
@@asmodeojung omg im pretty sure this is an exact quote from one of my profs, especially the "math math math goodbye" bit!! XD
Because most of us, regardless of how much work we put in, will not be able to operate anywhere near this genius's ability so we might as well look at boobs instead. We can study chess all day long, after five years we'll still get crushed by Carlson so what's the point?
@@johnvonhorn2942 Just for curiosity sake and your own enjoyment. It's not all about being the best, any kind of new knowledge is fun to gain
Because we're ignorant and good numerologist is hard to find.
Thank you dear professor.
I am a surgeon. I was bitten by the math bug last year due to stalwarts like you. Thanks for making me see beauty again in formal education.
Every time he's about to clearly and unambiguously explain something in a way the rest of us non-mathematicians could understand, his voice cuts out.
Deep state doesn't want u to understand it...
I know ;( it is so sad.
This is a great talk, thanks for your effort. FYI there are some short sections where the audio track becomes distorted, and one or two where words cannot be understood. Its accessibility would be helped by subtitles to cover those sections.
Thanks a lot, Prof. Borcherds! I actually found your explanation of vertex algebras very useful, because I know quantum field theory, and could relate the axioms to the operator product expansion!
Thank you for this guided tour of your amazing work!
It is a great talk !
Thumbs up for content, but the audio flakes out in spots and the contrast (i.e. legibility) of the text could have been better.
Richard da 🐐 no 🧢 (Seriously though, Prof. Borcherds is one of the most influential mathematician of the present age.)
"Shout out Rich-E B" -Migos vs. Nardwuar, 2015
This monstrous moonshine stuff is really fascinating. I'm just trying to find the connection to sqrt(163) and the fine structure constant ε0 in physics. Someone mentioned it to me, but I can't recall the details. Borcherds might know more about it.
Umbral moonshine actually was proven rather recently, I believe.
Thank you for this amazing talk. Do you have books you would recommend to learn more?
I believe "Vertex Operator Algebras and the Monster" (Frenkel, Lepowsky, Meurman) is a well-known book on this topic specifically. As he noted in the talk, "Vertex Algebras for Beginners" is an "introduction" to vertex algebras in general.
I too was going to recomend VOAs and the Monster. The introduction reads like a spy novel. (You can stop there though.)
I got through the entire video, thought it was interesting, then months later watched the Numberphile video on the Monster group. "Hmm, that name 'Richard Borcherds' seems familiar"...
It's amazing how string theory has actually had mathematical implications!
it's always been mathematical. :)
Hello smart people. If you understand this video I sincerely hope you are being paid well because I can’t imagine how many courses in math you’ve had to pay for
pay? what an american centric view
This is honestly understandable by someone with an undergraduate mathematics education with independent learning of group, representation, and algebraic vertex theory
If I watch the series on Group Theory, will I understand everything here?
No, but a much better understanding. Courses in number theory and representation theory would be rather helpful.
This video subject is considerably more difficult, but for most parts you will at least be able to understand what is being explained.
about the algebra product, though. there are a few more identities involving the inner product. and when two vectors alternate as a(ac) = (aa)c. then all possible vectors b associate like a(bc) = (ab)c. in other words, alternativity implies associativity.
the inner product actually creates a symmetric **trilinear** form with the algebra product. in other words, the inner product (ab, c) = (a, bc) is invariant under all permutations of a, b, and c.
also, John H. Conway simplified the construction significantly by incorporating the Parker loop into the construction in order resolve the sign problem. he also incorporated the fixed vector into the algebra product by treating it as an identity element. he also used double covers and fourfold convers of **three** involution centralisers and the normaliser of a specific fourgroup in the monster. rather than treating the centraliser of a **single** involution, he took centralisers of **all three** involutions of the fourgroup, and constructed the monster as the group generated by the three matrix groups that **each centralise a different** involution in the fourgroup. and the "three" algebra products defined over them are actually one and the same.
This is fascinating!
You should change your name to Ricardas Borcerdas.
WHAT
Using R for the group acting on a ring is a little confusing.
Hi. Does there exist a mapping of a set of Monster symmetries to those that are compatible with Calabi-Yau manifolds? I'm wondering if any symmetry relations that exist in M might manifest in lower dimensions, some subgroup of M, as (at least roughly) symmetries of the Standard Model and/or those of spacetime? We've got this beautiful, complex group that exists and touches so many branches of maths, makes me wonder how much it and it mysteries might manifest.
Griess is pronounced like Greece with a German sounding "r".
Griess is American, and the pronunciation of his surname is Americanized, to avoid "grease"
@@gresach I didn't know :( To German ears it sounds terrible, though :)
@@rainerausdemspring3584 Now you guys know how the non-germans feels when you guys talk.
@@aa-lr1jk I am German and have learned Latin, English and French. Now you guys know how Germans feel when you guys talk Latin, French or German :)
@@rainerausdemspring3584 Haha, touché (don't take it personal, its was meant as a joke).
KYU THAK RAHE HO
Scp 914
This is the 5 minutes problem , I am serious
So en.wikipedia.org/wiki/743_(number) or 744 could be zero, but just not as groupie. Root(744)? I vaguely remember discriminants of the 44 elliptics of character 1 modulo 3 being 18 of them. ...