Moonshine Beyond the Monster
The Bridge Connecting Algebra, Modular Forms and Physics
By Terry Gannon
Publisher: Cambridge University Press
Print Publication Year: 2006
Online Publication Date:August 2009
Online ISBN:9780511535116
Hardback ISBN:9780521835312
Paperback ISBN:9780521141888
Chapter DOI: http://dx.doi.org/10.1017/CBO9780511535116.001
Subjects: Theoretical Physics and Mathematical Physics, Mathematical Physics
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When you are collecting mushrooms, you only see the mushroom itself. But if you are a mycologist, you know that the real mushroom is in the earth. There's an enormous thing down there, and you just see the fruit, the body that you eat. In mathematics, the upper part of the mushroom corresponds to theorems that you see, but you don't see the things that are below, that is: problems, conjectures, mistakes, ideas, etc.
V. I. Arnold [17]
What my experience of mathematical work has taught me again and again, is that the proof always springs from the insight, and not the other way around – and that the insight itself has its source, first and foremost, in a delicate and obstinate feeling of the relevant entities and concepts and their mutual relations. The guiding thread is the inner coherence of the image which gradually emerges from the mist, as well as its consonance with what is known or foreshadowed from other sources – and it guides all the more surely as the ‘exigence’ of coherence is stronger and more delicate.
A. Grothendieck.
Interesting events (e.g. wars) always happen whenever different realisations of the same thing confront one another. When clarity and precision are added to the mix, we call this mathematics. In particular, the most exciting and significant moments in mathematics occur when we discover that seemingly unrelated phenomena are shadows cast by the same beast. This book studies one who has been recently awakened.
pp. i-vi
pp. vii-xii
pp. xiii-xiv
0 - Introduction: glimpses of the theory beneath Monstrous Moonshine : Read PDF
pp. 1-13
1 - Classical algebra : Read PDF
pp. 14-103
pp. 104-175
3 - Gold and brass: affine algebras and generalisations : Read PDF
pp. 176-225
4 - Conformal field theory: the physics of Moonshine : Read PDF
pp. 226-310
5 - Vertex operator algebras : Read PDF
pp. 311-353
6 - Modular group representations throughout the realm : Read PDF
pp. 354-401
7 - Monstrous Moonshine : Read PDF
pp. 402-434
Epilogue, or the squirrel who got away? : Read PDF
pp. 435-435
pp. 436-444
pp. 445-463
pp. 464-477