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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[m.alperenyasar]

I am not a mathematician nor a physicist but Prof. Richard Borcherds was so clear even I understood this topic. I'm really glad that I have found this video ^^

[j.mauricerojas]

What a beautifully clear talk! So nice to see a Fields medalist take the time to give such an accessible talk! Thank you!

[henrikljungstrand]

The techniques used for proving the classification of finite simple groups might be useful for proving similar results about Hopf algebras, and possibly some classes of loops that are well behaved enough like e.g. Left Bol loops (Moufang loops were surprisingly little more complicated than groups when it comes to simplicity).

[IsZomg]

At 18:20 he says the smallest non-cyclic group is order 60, but S3 is non-cyclic and has order 6?

[sasha-]

46:34 must be a floating point error or something why those are "almost integers" in some super computer

[jimmypk]

I hit pay dirt today! Instantly subscribed!

[nicholaswilliams]

Adam (blue shirt) had some great questions! Thanks, Adam, wherever you may be.

[fjfaase]

For John Conways water based 'computer' (actually more of a logic circuit), google for: This early computer was based on a urinal flush mechanism

[hyperduality]

Elliptic curves are dual to modular forms.
"Perpendicularity in hyperbolic space is measured in terms of duality" -- Professor Norman Wildberger.
Positive curvature is dual to negative curvature -- Gauss, Riemann geometry.
Gravitation is equivalent or dual to acceleration -- Einstein's happiest thought, the principle of equivalence (duality).
Fractals = self similarity, self equivalence = self duality!
The Klein bottle contains two mobius loops when cut in half -- self intersection = duality.
Energy is duality, duality is energy.
Time duality -- the future is dual to the past.

[richardboland]

OK cool.

So my next dnd adventure is going to feature radiolarians for sure.

😛

[adrianorizabal]

3 little blue boys and a brown guy brought me here

[davidwilkie]

Grouped conglomerations of prime-connection coordination in ONE-INFINITY Quantum-fields Mechanism of AM-FM QM-TIME Communication Completeness/Singularity positioning of logarithmic numberness condensation.
I Agree, in absolute principle.

[rossevans]

It saddens me that some stupid prank channel can garner millions of subscribers showcasing banal idiocy, but high quality pedagogy, is largely ignored. We really can't claim that we don't have exactly the kind of society we deserve.