Sporadic groups | Moonshine theory | Group theory
In mathematics, monstrous moonshine, or moonshine theory, is the unexpected connection between the monster group M and modular functions, in particular, the j function. The term was coined by John Conway and Simon P. Norton in 1979. The monstrous moonshine is now known to be underlain by a vertex operator algebra called the moonshine module (or monster vertex algebra) constructed by Igor Frenkel, James Lepowsky, and Arne Meurman in 1988, which has the monster group as its group of symmetries. This vertex operator algebra is commonly interpreted as a structure underlying a two-dimensional conformal field theory, allowing physics to form a bridge between two mathematical areas. The conjectures made by Conway and Norton were proven by Richard Borcherds for the moonshine module in 1992 using the no-ghost theorem from string theory and the theory of vertex operator algebras and generalized Kac–Moody algebras. (Wikipedia).
This is an expository talk on the monstrous moonshine conjectures about the monster simple group in mathematics.
From playlist Math talks
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From playlist Moonshiners
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From playlist Moonshiners
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From playlist Moonshiners
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From playlist Moonshiners
Can't you just feel the Moonshine? - Ken Ono (Emory University) [2017]
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From playlist Number Theory
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DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra
From playlist Group Theory and Computational Methods
A guide to moonshine - John Duncan
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From playlist Mathematics
Tathagata Basak: A monstrous(?) complex hyperbolic orbifold
I will report on progress with Daniel Allcock on the ”Monstrous Proposal”, namely the conjecture: Complex hyperbolic 13-space, modulo a particular discrete group, and with orbifold structure changed in a simple way, has fundamental group equal to (MxM)(semidirect)2, where M is the Monster
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From playlist Mathematics
Math talk: Sporadic groups and number theory
This talk was the introduction to the Berkeley graduate number theory discussion seminar on 2020-10-28, and the aim was to explain why number theorists might be interested in sporadic simple groups. We give a brief summary of monstrous moonshine relating sporadic groups to modular functi
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GT23. Composition and Classification
Abstract Algebra: We use composition series as another technique for studying finite groups, which leads to the notion of solvable groups and puts the focus on simple groups. From there, we survey the classification of finite simple groups and the Monster group.
From playlist Abstract Algebra
This is an experimental video where I give answers to the (mostly) mathematical questions asked by viewers.
From playlist Math talks
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This is an informal talk on sporadic groups given to the Archimedeans (the Cambridge undergraduate mathematical society). It discusses the classification of finite simple groups and some of the sporadic groups, and finishes by briefly describing monstrous moonshine. For other Archimedeans
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